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BUNDLE THEOREM

  • Bundle theorem
  • In Euclidean geometry, the bundle theorem is a statement about six circles and eight points in the Euclidean plane. In general incidence geometry, it is

    Bundle theorem

    Bundle theorem

    Bundle_theorem

  • Fiber bundle construction theorem
  • Constructs a fiber bundle from a base space, fiber and a set of transition functions

    In mathematics, the fiber bundle construction theorem is a theorem which constructs a fiber bundle with a structure group from a given base space, fiber

    Fiber bundle construction theorem

    Fiber bundle construction theorem

    Fiber_bundle_construction_theorem

  • Canonical bundle
  • Concept in algebraic geometry

    canonical bundle of a non-singular algebraic variety V {\displaystyle V} of dimension n {\displaystyle n} over a field is the line bundle Ω n = ω {\displaystyle

    Canonical bundle

    Canonical_bundle

  • Grothendieck–Riemann–Roch theorem
  • Result in algebraic geometry

    Riemann–Roch theorem for line bundles on compact Riemann surfaces. Riemann–Roch type theorems relate Euler characteristics of the cohomology of a vector bundle with

    Grothendieck–Riemann–Roch theorem

    Grothendieck–Riemann–Roch theorem

    Grothendieck–Riemann–Roch_theorem

  • Holomorphic vector bundle
  • Complex vector bundle on a complex manifold

    In mathematics, a holomorphic vector bundle is a complex vector bundle over a complex manifold X such that the total space E is a complex manifold and

    Holomorphic vector bundle

    Holomorphic_vector_bundle

  • Atiyah–Singer index theorem
  • Mathematical result in differential geometry

    signature operators with values in vector bundles are topological invariants. 1984: Teleman establishes the index theorem on topological manifolds. 1986: Alain

    Atiyah–Singer index theorem

    Atiyah–Singer_index_theorem

  • Hirzebruch–Riemann–Roch theorem
  • On the Euler characteristic of a holomorphic vector bundle on a compact complex manifold

    theorem proved about three years later. The Hirzebruch–Riemann–Roch theorem applies to any holomorphic vector bundle E on a compact complex

    Hirzebruch–Riemann–Roch theorem

    Hirzebruch–Riemann–Roch_theorem

  • Ample line bundle
  • Concept in algebraic geometry

    canonical bundle is anti-ample Matsusaka's big theorem Divisorial scheme: a scheme admitting an ample family of line bundles Holomorphic vector bundle Kodaira

    Ample line bundle

    Ample_line_bundle

  • Birkhoff–Grothendieck theorem
  • Classifies holomorphic vector bundles over the complex projective line

    Birkhoff–Grothendieck theorem classifies holomorphic vector bundles over the complex projective line. In particular every holomorphic vector bundle over C P 1 {\displaystyle

    Birkhoff–Grothendieck theorem

    Birkhoff–Grothendieck_theorem

  • Vector bundle
  • Mathematical parametrization of vector spaces by another space

    Tangent bundles are not, in general, trivial bundles. For example, the tangent bundle of the sphere is non-trivial by the hairy ball theorem. In general

    Vector bundle

    Vector bundle

    Vector_bundle

  • Fundamental theorems of welfare economics
  • Complete, full information, perfectly competitive markets are Pareto efficient

    There are two fundamental theorems of welfare economics. The first states that in economic equilibrium, a set of complete markets, with complete information

    Fundamental theorems of welfare economics

    Fundamental_theorems_of_welfare_economics

  • Riemann–Roch theorem
  • Relation between genus, degree, and dimension of function spaces over surfaces

    The Riemann–Roch theorem is an important theorem in mathematics, specifically in complex analysis and algebraic geometry, for the computation of the dimension

    Riemann–Roch theorem

    Riemann–Roch_theorem

  • Universal bundle
  • The following Theorem is a corollary of the above Proposition. Theorem. If M is a paracompact manifold and P → M is a principal G-bundle, then there exists

    Universal bundle

    Universal_bundle

  • Holonomy
  • Concept in differential geometry

    decomposition theorem, a principle for splitting a Riemannian manifold into a Cartesian product of Riemannian manifolds by splitting the tangent bundle into irreducible

    Holonomy

    Holonomy

    Holonomy

  • Beauville–Laszlo theorem
  • Lets one glue 2 sheaves over an infinitesimal neighborhood of an algebraic curve point

    the theorem admits a global statement of the same nature. The version of this statement that the authors found noteworthy concerns vector bundles: Theorem:

    Beauville–Laszlo theorem

    Beauville–Laszlo_theorem

  • Principal bundle
  • Fiber bundle whose fibers are group torsors

    one may reconstruct the original principal bundle. This is an example of the fiber bundle construction theorem. For any x ∈ Ui ∩ Uj we have s j ( x ) =

    Principal bundle

    Principal_bundle

  • Chern–Gauss–Bonnet theorem
  • Ties Euler characteristic of a closed even-dimensional Riemannian manifold to curvature

    product with the Euler class of the tangent bundle T M {\displaystyle TM} . In 1944, the general theorem was first proved by S. S. Chern in a classic

    Chern–Gauss–Bonnet theorem

    Chern–Gauss–Bonnet_theorem

  • Frobenius theorem (differential topology)
  • On finding a maximal set of solutions of a system of first-order homogeneous linear PDEs

    theorem gives necessary and sufficient integrability conditions for the existence of a foliation by maximal integral manifolds whose tangent bundles are

    Frobenius theorem (differential topology)

    Frobenius theorem (differential topology)

    Frobenius_theorem_(differential_topology)

  • Borel–Weil–Bott theorem
  • Basic result in the representation theory of Lie groups

    vector bundles, and, more generally, from higher sheaf cohomology groups associated to such bundles. It is built on the earlier Borel–Weil theorem of Armand

    Borel–Weil–Bott theorem

    Borel–Weil–Bott_theorem

  • Fiber bundle
  • Continuous surjection satisfying a local triviality condition

    In mathematics, and particularly topology, a fiber bundle (Commonwealth English: fibre bundle) is a space that is locally a product space, but globally

    Fiber bundle

    Fiber bundle

    Fiber_bundle

  • Seesaw theorem
  • the seesaw theorem, or seesaw principle, says roughly that a limit of trivial line bundles over complete varieties is a trivial line bundle. It was introduced

    Seesaw theorem

    Seesaw_theorem

  • Miquel's theorem
  • Concerns 3 circles through triples of points on the vertices and sides of a triangle

    edges of the tetrahedron intersect in a common point. Bundle theorem Clifford's circle theorems Miquel configuration A high school teacher in the French

    Miquel's theorem

    Miquel's theorem

    Miquel's_theorem

  • Serre–Swan theorem
  • Relates the geometric vector bundles to algebraic projective modules

    algebraic geometry, the Serre–Swan theorem, also called Swan's theorem, relates the geometric notion of vector bundles to the algebraic concept of projective

    Serre–Swan theorem

    Serre–Swan_theorem

  • Frame bundle
  • Principal bundle associated to a vector bundle

    In mathematics, a frame bundle is a principal fiber bundle F ( E ) {\displaystyle F(E)} associated with any vector bundle E {\displaystyle E} . The fiber

    Frame bundle

    Frame bundle

    Frame_bundle

  • Kawamata–Viehweg vanishing theorem
  • The theorem states that if L is a big nef line bundle (for example, an ample line bundle) on a complex projective manifold with canonical line bundle K

    Kawamata–Viehweg vanishing theorem

    Kawamata–Viehweg_vanishing_theorem

  • Narasimhan–Seshadri theorem
  • Mathematic theorem about Riemann surfaces

    mathematics, the Narasimhan–Seshadri theorem, proved by Narasimhan and Seshadri (1965), says that a holomorphic vector bundle over a compact Riemann surface

    Narasimhan–Seshadri theorem

    Narasimhan–Seshadri_theorem

  • Yang–Mills equations
  • Partial differential equations whose solutions are instantons

    of partial differential equations for a connection on a vector bundle or principal bundle. They arise in physics as the Euler–Lagrange equations of the

    Yang–Mills equations

    Yang–Mills equations

    Yang–Mills_equations

  • Soul theorem
  • Complete manifolds of non-negative sectional curvature largely reduce to the compact case

    In mathematics, the soul theorem is a theorem of Riemannian geometry that largely reduces the study of complete manifolds of non-negative sectional curvature

    Soul theorem

    Soul_theorem

  • Serre duality
  • Theorem in algebraic geometry

    duality in topology, with the canonical line bundle replacing the orientation sheaf. The Serre duality theorem is also true in complex geometry more generally

    Serre duality

    Serre_duality

  • Nef line bundle
  • Concept in algebraic geometry

    geometry, a line bundle on a projective variety is nef if it has nonnegative degree on every curve in the variety. The classes of nef line bundles are described

    Nef line bundle

    Nef_line_bundle

  • Dual abelian variety
  • Mukai's theorem is then as follows. Theorem: Let A be an abelian variety of dimension g and P A {\displaystyle P_{A}} the Poincare line bundle on A × A

    Dual abelian variety

    Dual_abelian_variety

  • Kobayashi–Hitchin correspondence
  • Vector bundles theorem

    Donaldson–Uhlenbeck–Yau theorem) relates stable vector bundles over a complex manifold to Einstein–Hermitian vector bundles. The correspondence is named

    Kobayashi–Hitchin correspondence

    Kobayashi–Hitchin_correspondence

  • Normal bundle
  • Concept in mathematics

    a field of mathematics, a normal bundle is a particular kind of vector bundle, complementary to the tangent bundle, and coming from an embedding (or

    Normal bundle

    Normal_bundle

  • Kodaira vanishing theorem
  • Gives general conditions under which sheaf cohomology groups with indices > 0 are zero

    theorem. The statement of Kunihiko Kodaira's result is that if M is a compact Kähler manifold of complex dimension n, L any holomorphic line bundle on

    Kodaira vanishing theorem

    Kodaira_vanishing_theorem

  • Matsusaka's big theorem
  • In algebraic geometry, given an ample line bundle L on a compact complex manifold X, Matsusaka's big theorem gives an integer m, depending only on the

    Matsusaka's big theorem

    Matsusaka's_big_theorem

  • Le Potier's vanishing theorem
  • Generalizes the Kodaira vanishing theorem for ample vector bundle

    geometry, Le Potier's vanishing theorem is an extension of the Kodaira vanishing theorem, on vector bundles. The theorem states the following Le Potier

    Le Potier's vanishing theorem

    Le_Potier's_vanishing_theorem

  • Principal U(1)-bundle
  • Special type of principal bundle

    \operatorname {U} (1)} -bundles (or principal SO ⁡ ( 2 ) {\displaystyle \operatorname {SO} (2)} -bundles) are special principal bundles with the first unitary

    Principal U(1)-bundle

    Principal U(1)-bundle

    Principal_U(1)-bundle

  • Arakelov theory
  • Mathematical theory

    is a proper morphism from X to Y and E is a vector bundle over f. The arithmetic Riemann–Roch theorem is similar, except that the Todd class gets multiplied

    Arakelov theory

    Arakelov_theory

  • Associated bundle
  • Fiber bundle

    condition. Hence, by the existence part of the fiber bundle construction theorem, this produces a fiber bundle E ′ {\displaystyle E'} with fiber F ′ {\displaystyle

    Associated bundle

    Associated_bundle

  • Quillen–Suslin theorem
  • Commutative algebra theorem

    setting it is a statement about the triviality of vector bundles on affine space. The theorem states that every finitely generated projective module over

    Quillen–Suslin theorem

    Quillen–Suslin_theorem

  • Kodaira embedding theorem
  • Characterises non-singular projective varieties amongst compact Kähler manifolds

    In mathematics, the Kodaira embedding theorem characterises non-singular projective varieties, over the complex numbers, amongst compact Kähler manifolds

    Kodaira embedding theorem

    Kodaira_embedding_theorem

  • Jeff Kahn (mathematician)
  • American mathematician

    advisor Dijen K. Ray-Chaudhuri. In 1980, he showed the importance of the bundle theorem for ovoidal Möbius planes. In 1993, together with Gil Kalai, he disproved

    Jeff Kahn (mathematician)

    Jeff Kahn (mathematician)

    Jeff_Kahn_(mathematician)

  • Coherent sheaf
  • Generalization of vector bundles

    Riemann–Roch theorem. Picard group Divisor (algebraic geometry) Reflexive sheaf Quot scheme Twisted sheaf Essentially finite vector bundle Bundle of principal

    Coherent sheaf

    Coherent_sheaf

  • Tangent bundle
  • Tangent spaces of a manifold

    A tangent bundle is the collection of all of the tangent spaces for all points on a manifold, structured in a way that it forms a new manifold itself.

    Tangent bundle

    Tangent bundle

    Tangent_bundle

  • Gauge theory (mathematics)
  • Study of vector bundles, principal bundles, and fibre bundles

    fibre bundle construction theorem and the same process works for any fibre bundle described by transition functions, not just principal bundles or vector

    Gauge theory (mathematics)

    Gauge_theory_(mathematics)

  • Projective bundle
  • Fiber bundle whose fibers are projective spaces

    projective bundle is a fiber bundle whose fibers are projective spaces. By definition, a scheme X over a Noetherian scheme S is a Pn-bundle if it is locally

    Projective bundle

    Projective_bundle

  • Representation theorem
  • Proof that every structure with certain properties is isomorphic to another structure

    In mathematics, representation theorem is a theorem that states that every abstract structure with certain properties is isomorphic to another (abstract

    Representation theorem

    Representation_theorem

  • Dual bundle
  • Mathematical operation on vector bundles

    The dual bundle E ∗ {\displaystyle E^{*}} is then constructed using the fiber bundle construction theorem. As particular cases: The dual bundle of an associated

    Dual bundle

    Dual_bundle

  • Cotangent bundle
  • Vector bundle of cotangent spaces at every point in a manifold

    mathematics, especially differential geometry, the cotangent bundle of a smooth manifold is the vector bundle of all the cotangent spaces at every point in the manifold

    Cotangent bundle

    Cotangent_bundle

  • Coherent sheaf cohomology
  • Concept in algebraic geometry

    Riemann–Roch theorem and its generalizations, the Hirzebruch–Riemann–Roch theorem and the Grothendieck–Riemann–Roch theorem. For example, if L is a line bundle on

    Coherent sheaf cohomology

    Coherent_sheaf_cohomology

  • Nakano vanishing theorem
  • Generalizes the Kodaira vanishing theorem

    study of vector bundles over complex Kähler manifolds, the Nakano vanishing theorem, sometimes called the Akizuki–Nakano vanishing theorem, generalizes the

    Nakano vanishing theorem

    Nakano_vanishing_theorem

  • Fano surface
  • of the universal rank 2 bundle on G. We have the: Tangent bundle Theorem (Fano, Clemens-Griffiths, Tyurin): The tangent bundle of S is isomorphic to U

    Fano surface

    Fano_surface

  • Tautological bundle
  • Vector bundle existing over a Grassmannian

    In mathematics, the tautological bundle is a vector bundle occurring over a Grassmannian in a natural tautological way: for a Grassmannian of k {\displaystyle

    Tautological bundle

    Tautological_bundle

  • Donaldson's theorem
  • On when a definite intersection form of a smooth 4-manifold is diagonalizable

    \operatorname {SU} (2)} -bundle P {\displaystyle P} over the four-manifold X {\displaystyle X} . By the Atiyah–Singer index theorem, the dimension of the

    Donaldson's theorem

    Donaldson's_theorem

  • Principal SU(2)-bundle
  • Special type of principal bundle

    \operatorname {SU} (2)} -bundles are used in many areas of mathematics, for example for the Fields Medal winning proof of Donaldson's theorem or instanton Floer

    Principal SU(2)-bundle

    Principal_SU(2)-bundle

  • Procesi bundle
  • Procesi bundles on any given symplectic resolution obtained by Hamiltonian reduction. As a result of their use in the proof of the n! theorem, Procesi

    Procesi bundle

    Procesi_bundle

  • List of differential geometry topics
  • pushforward (differential) jet (mathematics) Contact (mathematics) jet bundle Frobenius theorem (differential topology) Integral curve Diffeomorphism Large diffeomorphism

    List of differential geometry topics

    List_of_differential_geometry_topics

  • Stable normal bundle
  • of a manifold in Euclidean space (provided by the theorem of Hassler Whitney), it has a normal bundle. The embedding is not unique, but for high dimension

    Stable normal bundle

    Stable_normal_bundle

  • Noether's theorem
  • Statement relating differentiable symmetries to conserved quantities

    Noether's theorem states that every continuous symmetry of the action of a physical system with conservative forces has a corresponding conservation law

    Noether's theorem

    Noether's theorem

    Noether's_theorem

  • Thom space
  • Topological space associated to a vector bundle

    \gamma ^{n}\to BO(n)} for the universal vector bundle of rank n. The sequence forms a spectrum. A theorem of Thom says that π ∗ ( M O ) {\displaystyle \pi

    Thom space

    Thom_space

  • List of circle topics
  • targets Bundle theorem Butterfly theorem – About the midpoint of a chord of a circle, through which two other chords are drawn Carnot's theorem – Theorem in

    List of circle topics

    List of circle topics

    List_of_circle_topics

  • Uhlenbeck's singularity theorem
  • Singularity theorem in Yang–Mills theory

    geometry and in particular Yang–Mills theory, Uhlenbeck's singularity theorem is a result allowing the removal of a singularity of a four-dimensional

    Uhlenbeck's singularity theorem

    Uhlenbeck's_singularity_theorem

  • K-theory
  • Branch of mathematics

    K^{0}(X)} . We can use the Serre–Swan theorem and some algebra to get an alternative description of vector bundles over X {\displaystyle X} as projective

    K-theory

    K-theory

  • Nonabelian Hodge correspondence
  • Correspondsnce between Higgs bundles and fundamental group representations

    Higgs bundles and representations of the fundamental group of a smooth, projective complex algebraic variety, or a compact Kähler manifold. The theorem can

    Nonabelian Hodge correspondence

    Nonabelian_Hodge_correspondence

  • Lefschetz hyperplane theorem
  • Theorem in algebraic geometry

    in algebraic geometry and algebraic topology, the Lefschetz hyperplane theorem is a precise statement of certain relations between the shape of an algebraic

    Lefschetz hyperplane theorem

    Lefschetz_hyperplane_theorem

  • Atiyah–Bott fixed-point theorem
  • Fixed-point theorem for smooth manifolds

    vector bundles, generalizing the de Rham complex constructed from smooth differential forms which appears in the original Lefschetz fixed-point theorem. The

    Atiyah–Bott fixed-point theorem

    Atiyah–Bott_fixed-point_theorem

  • Bolzano–Weierstrass theorem
  • Bounded sequence in finite-dimensional Euclidean space has a convergent subsequence

    In mathematics, specifically in real analysis, the Bolzano–Weierstrass theorem, named after Bernard Bolzano and Karl Weierstrass, is a fundamental result

    Bolzano–Weierstrass theorem

    Bolzano–Weierstrass_theorem

  • Leray–Hirsch theorem
  • Relates the homology of a fiber bundle with the homologies of its base and fiber

    In mathematics, the Leray–Hirsch theorem is a basic result on the algebraic topology of fiber bundles. It is named after Jean Leray and Guy Hirsch, who

    Leray–Hirsch theorem

    Leray–Hirsch_theorem

  • Nadel vanishing theorem
  • Vanishing theorem for multiplier ideals

    Matsumura, Shin-Ichi (2015). "A Nadel vanishing theorem for metrics with minimal singularities on big line bundles". Advances in Mathematics. 280: 188–207. arXiv:1306

    Nadel vanishing theorem

    Nadel_vanishing_theorem

  • Chern class
  • Characteristic classes of vector bundles

    bundle has. The Chern classes offer some information about this through, for instance, the Riemann–Roch theorem and the Atiyah–Singer index theorem.

    Chern class

    Chern_class

  • Splitting principle
  • Mathematical technique for vector bundles

    following theorem. This theorem holds for complex vector bundles and cohomology with integer coefficients. It also holds for real vector bundles and cohomology

    Splitting principle

    Splitting_principle

  • Kuiper's theorem
  • Result on the topology of operators on an infinite-dimensional, complex Hilbert space

    vector bundles (see Classifying space for U(n)). A deeper application coming from Kuiper's theorem is the proof of the Atiyah–Jänich theorem (after Klaus

    Kuiper's theorem

    Kuiper's_theorem

  • Vector bundles on algebraic curves
  • classification of vector bundles on elliptic curves. The Riemann–Roch theorem for vector bundles was proved by Weil (1938), before the 'vector bundle' concept had

    Vector bundles on algebraic curves

    Vector_bundles_on_algebraic_curves

  • Möbius plane
  • (see quadratic set). Ovoidal Möbius planes are characterized by the bundle theorem. A block design with the parameters of the one-point extension of a

    Möbius plane

    Möbius_plane

  • Theorem of the cube
  • In mathematics, the theorem of the cube is a condition for a line bundle over a product of three complete varieties to be trivial. It was a principle discovered

    Theorem of the cube

    Theorem_of_the_cube

  • Michael Atiyah
  • British-Lebanese mathematician (1929–2019)

    (instantons) for any principal bundle over a compact 4-dimensional Riemannian manifold (the Atiyah–Hitchin–Singer theorem). For example, the dimension of

    Michael Atiyah

    Michael Atiyah

    Michael_Atiyah

  • Riemann–Roch theorem for smooth manifolds
  • Version without requiring the smooth manifolds involved to carry a complex structure

    vector bundle V over X, then the Gysin maps are just the Thom isomorphism. Then, using the splitting principle, it suffices to check the theorem via explicit

    Riemann–Roch theorem for smooth manifolds

    Riemann–Roch_theorem_for_smooth_manifolds

  • Line bundle
  • Vector bundle of rank 1

    In mathematics, a line bundle expresses the concept of a line that varies from point to point of a space. For example, a curve in the plane having a tangent

    Line bundle

    Line_bundle

  • List of algebraic topology topics
  • Algebraic topology uses abstract algebra to study topological spaces

    representability theorem Eilenberg–MacLane space Fibre bundle Möbius strip Line bundle Canonical line bundle Vector bundle Associated bundle Fibration Hopf bundle Classifying

    List of algebraic topology topics

    List_of_algebraic_topology_topics

  • Wilson's theorem
  • Theorem on prime numbers

    In algebra and number theory, Wilson's theorem states that a natural number n > 1 is a prime number if and only if the product of all the positive integers

    Wilson's theorem

    Wilson's_theorem

  • Revealed preference
  • Economic concept

    datasets. For instance, if two bundles both maximize utility at the same budget (as in the GARP figure), Afriat's Theorem ensures a utility function exists

    Revealed preference

    Revealed_preference

  • Local nonsatiation
  • Consumer preferences property

    also a key assumption for the First welfare theorem. An indifference curve is a set of all commodity bundles providing consumers with the same level of

    Local nonsatiation

    Local nonsatiation

    Local_nonsatiation

  • List of things named after Stefan Banach
  • *-algebra Banach algebra cohomology Banach bundle Banach bundle (non-commutative geometry) Banach fixed-point theorem Banach game Banach lattice Banach limit

    List of things named after Stefan Banach

    List_of_things_named_after_Stefan_Banach

  • Plumbing (mathematics)
  • Way to create new manifolds out of disk bundles

    _{M_{B}^{4k}}\rightarrow \xi } is a bundle map from the stable normal bundle of the Milnor manifold to a certain stable vector bundle. A crucial theorem for the development

    Plumbing (mathematics)

    Plumbing (mathematics)

    Plumbing_(mathematics)

  • Differentiable manifold
  • Manifold upon which it is possible to perform calculus

    fundamental theorems of integral calculus in several variables—namely Green's theorem, the divergence theorem, and Stokes' theorem—generalize to a theorem (also

    Differentiable manifold

    Differentiable manifold

    Differentiable_manifold

  • Reider's theorem
  • In algebraic geometry, Reider's theorem gives conditions for a line bundle on a projective surface to be very ample. Let D be a nef divisor on a smooth

    Reider's theorem

    Reider's_theorem

  • Riemann–Roch-type theorem
  • Theorem in geometry

    of vector bundles on X; it is independent of the factorization and is called the virtual tangent bundle of f. Then the Riemann–Roch theorem then amounts

    Riemann–Roch-type theorem

    Riemann–Roch-type_theorem

  • Appell–Humbert theorem
  • Describes the line bundles on a complex torus or complex abelian variety

    In mathematics, the Appell–Humbert theorem describes the line bundles on a complex torus or complex abelian variety. It was proved for 2-dimensional tori

    Appell–Humbert theorem

    Appell–Humbert_theorem

  • Todd class
  • Characteristic class in algebraic topology

    as a conormal bundle does to a normal bundle. The Todd class plays a fundamental role in generalising the classical Riemann–Roch theorem to higher dimensions

    Todd class

    Todd_class

  • Hirzebruch signature theorem
  • Gives the signature of a smooth compact oriented manifold in terms of Pontryagin numbers

    an area of mathematics, the Hirzebruch signature theorem (sometimes called the Hirzebruch index theorem) is Friedrich Hirzebruch's 1954 result expressing

    Hirzebruch signature theorem

    Hirzebruch_signature_theorem

  • Complex vector bundle
  • complex vector bundle is a vector bundle whose fibers are complex vector spaces. Any complex vector bundle can be viewed as a real vector bundle through the

    Complex vector bundle

    Complex_vector_bundle

  • Almost complex manifold
  • Smooth manifold

    J^{2}=-1} when regarded as a vector bundle isomorphism J : T M → T M {\displaystyle J\colon TM\to TM} on the tangent bundle. A manifold equipped with an almost

    Almost complex manifold

    Almost_complex_manifold

  • Riemann–Roch theorem for surfaces
  • Mathematical theorem

    In mathematics, the Riemann–Roch theorem for surfaces describes the dimension of linear systems on an algebraic surface. The classical form of it was

    Riemann–Roch theorem for surfaces

    Riemann–Roch_theorem_for_surfaces

  • Vertical and horizontal bundles
  • Mathematics concept

    vertical bundle and the horizontal bundle are vector bundles associated to a smooth fiber bundle. More precisely, given a smooth fiber bundle π : E → B

    Vertical and horizontal bundles

    Vertical and horizontal bundles

    Vertical_and_horizontal_bundles

  • Determinant line bundle
  • Construction for vector bundles

    geometry, the determinant line bundle is a construction, which assigns every vector bundle over paracompact spaces a line bundle. Its name comes from using

    Determinant line bundle

    Determinant_line_bundle

  • Topology
  • Branch of mathematics

    Königsberg problem and polyhedron formula are arguably the field's first theorems. The term topology was introduced by Johann Benedict Listing in the 19th

    Topology

    Topology

    Topology

  • Jumping line
  • lines of a vector bundle form a proper closed subset of the Grassmannian of all lines of projective space. The Birkhoff–Grothendieck theorem classifies the

    Jumping line

    Jumping_line

  • Lagrangian system
  • Pair in mathematics

    Lagrangian mechanics Calculus of variations Noether's theorem Noether identities Jet bundle Jet (mathematics) Variational bicomplex Sardanashvily 2013

    Lagrangian system

    Lagrangian_system

  • Connection (vector bundle)
  • Defines a notion of parallel transport on a bundle

    gauge theory, a connection on a fiber bundle is a device that defines a notion of parallel transport on the bundle; that is, a way to "connect" or identify

    Connection (vector bundle)

    Connection_(vector_bundle)

  • Contact geometry
  • Branch of geometry

    C_{2n}M} , the 2 n {\displaystyle 2n} -th contact bundle of M {\displaystyle M} . By Darboux's theorem, all contact structures of the same dimension are

    Contact geometry

    Contact_geometry

AI & ChatGPT searchs for online references containing BUNDLE THEOREM

BUNDLE THEOREM

AI search references containing BUNDLE THEOREM

BUNDLE THEOREM

  • Bonde
  • Surname or Lastname

    English

    Bonde

    English : variant spelling of Bond.Scandinavian : status name for a farmer, from Old Norse bóndi ‘farmer’. Compare Bond. In Sweden Bonde is both a personal name and the name of an old aristocratic family.Norwegian : habitational name from a farmstead named Bonde, from Old Norse bóndi ‘farmer’ + vin ‘meadow’.

    Bonde

  • Windle
  • Surname or Lastname

    English (Lancashire and Yorkshire)

    Windle

    English (Lancashire and Yorkshire) : habitational name from Windhill in West Yorkshire or Windle in Lancashire, both named from Old English wind ‘wind’ + hyll ‘hill’, i.e. a mound exposed to fierce gusts. There is a Windhill in Kent (with the same etymology), but this does not appear to have contributed significantly to the modern surname.

    Windle

  • Bunte
  • Surname or Lastname

    German (Bünte)

    Bunte

    German (Bünte) : most likely a variant of Bünde (see Bunde 2).English : variant spelling of Bunt.

    Bunte

  • Hundley
  • Surname or Lastname

    English (Worcestershire)

    Hundley

    English (Worcestershire) : probably a variant of Hindley or Handley.

    Hundley

  • Kindle
  • Surname or Lastname

    English

    Kindle

    English : variant of Kendall.Variant of German Kindel.

    Kindle

  • Trundle
  • Surname or Lastname

    English (Essex, Cambridgeshire)

    Trundle

    English (Essex, Cambridgeshire) : possibly a variant of Trendall, a topographic name for someone who lived by a well, earhwork, stone circle, or other circular feature, from Middle English trendel, trandle ‘circle’ (Old English trendel).Possibly an altered spelling of South German Tröndle, a variant of Trendle, a nickname for a tearful person, from Träne ‘tear’ + the diminutive suffix -l.

    Trundle

  • Bendle
  • Surname or Lastname

    English (mainly Wales)

    Bendle

    English (mainly Wales) : variant of Benthall.In some cases, probably an altered spelling of German Bendel.

    Bendle

  • Huddle
  • Surname or Lastname

    English

    Huddle

    English : from a pet form of the medieval personal name Hudde (see Hutt 1).

    Huddle

  • Rundle
  • Surname or Lastname

    English

    Rundle

    English : variant of Rundell.Respelling of German Rundel.

    Rundle

  • Hurdle
  • Surname or Lastname

    English

    Hurdle

    English : probably a metonymic occupational name for a hurdle maker, from Middle English herdle, hurdel ‘hurdle’.

    Hurdle

  • Brindle
  • Surname or Lastname

    English (Lancashire)

    Brindle

    English (Lancashire) : habitational name from a place in Lancashire named Brindle, from Old English burna ‘stream’ + hyll ‘hill’.Altered spelling of South German Brindl, Bründl, a topographic name for someone who lived by a spring or stream, from a diminutive of Middle High German brun(ne) ‘spring’, ‘stream’, or of Brendle or Brendel.

    Brindle

  • Hindle
  • Surname or Lastname

    English (Lancashire)

    Hindle

    English (Lancashire) : topographic name from Old English hind ‘female deer’ + Old English dæl ‘valley’.English (Lancashire) : habitational name from a place in the parish of Whalley, Lancashire, so called from the same first element + Old English hyll ‘hill’.

    Hindle

  • Beedle
  • Surname or Lastname

    English

    Beedle

    English : variant spelling of Beadle.

    Beedle

  • Kendle
  • Surname or Lastname

    English

    Kendle

    English : variant spelling of Kendall.South German : possibly from Kindel or Kindl (from a diminutive of Middle High German kint ‘child’), a nickname for a childish or childlike person.Possibly an altered spelling of German Kendler, variant of Kandler.

    Kendle

  • Beadle
  • Surname or Lastname

    English

    Beadle

    English : occupational name for a medieval court official, from Middle English bedele (Old English bydel, reinforced by Old French bedel). The word is of Germanic origin, and akin to Old English bēodan ‘to command’ and Old High German bodo ‘messenger’. In the Middle Ages a beadle in England and France was a junior official of a court of justice, responsible for acting as an usher in a court, carrying the mace in processions in front of a justice, delivering official notices, making proclamations (as a sort of town crier), and so on. By Shakespeare’s day a beadle was a sort of village constable, appointed by the parish to keep order.

    Beadle

  • Durapa
  • Boy/Male

    Indian

    Durapa

    Bundle of Joy

    Durapa

  • Bodle
  • Surname or Lastname

    English

    Bodle

    English : topographic name for someone who lived or worked at a particular large house, from Old English boðl, botl ‘dwelling house’, ‘hall’, or a habitational name for someone who came from a place named with this element, probably Bodle Street near Hailsham, Sussex.

    Bodle

  • Budde
  • Surname or Lastname

    North German

    Budde

    North German : metonymic occupational name for a cooper, from Middle Low German budde ‘tub’, ‘vat’. Compare Buettner.German and Danish : from a derivative of the Germanic personal name Bodo, cognate with English Budd.English : variant spelling of Budd.

    Budde

  • Ruddle
  • Surname or Lastname

    English

    Ruddle

    English : nickname from a diminutive of Rudd ‘red’.English : habitational name from a place called Ruddle, near Newnham in Gloucestershire.

    Ruddle

  • Yandle
  • Surname or Lastname

    English

    Yandle

    English : variant of Yandell.

    Yandle

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Online names & meanings

  • Randy
  • Girl/Female

    Latin American

    Randy

    or Mirabel: Worthy of admiration; wonderful; marvelous.

  • Aacharya
  • Boy/Male

    Indian

    Aacharya

    Teacher

  • Farouk |
  • Boy/Male

    Muslim

    Farouk |

    Knowing right from wrong

  • Ghatiya |
  • Girl/Female

    Muslim

    Ghatiya |

    Dynamic, Moving

  • Brajesh
  • Boy/Male

    Bengali, Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Sanskrit, Telugu, Traditional

    Brajesh

    Lord of Braj Land

  • Pradhan | ப்ரதாந
  • Boy/Male

    Tamil

    Pradhan | ப்ரதாந

    Leader

  • Hurlbart
  • Boy/Male

    British, English, German

    Hurlbart

    Army Strong

  • Atish
  • Boy/Male

    Hindu

    Atish

    Kind, Explosive, A dynamic person

  • HUGON
  • Male

    French

    HUGON

    Old form of French Hugues, HUGON means "heart," "mind," or "spirit."

  • RONALDO
  • Male

    Portuguese

    RONALDO

    Portuguese form of Latin Reynaldus, RONALDO means "wise ruler."

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AI searchs for Acronyms & meanings containing BUNDLE THEOREM

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Other words and meanings similar to

BUNDLE THEOREM

AI search in online dictionary sources & meanings containing BUNDLE THEOREM

BUNDLE THEOREM

  • Bundle
  • v. t.

    To tie or bind in a bundle or roll.

  • Puddle
  • v. t.

    To make impervious to liquids by means of puddle; to apply puddle to.

  • Huddle
  • v. t.

    To do, make, or put, in haste or roughly; hence, to do imperfectly; -- usually with a following preposition or adverb; as, to huddle on; to huddle up; to huddle together.

  • Ruddle
  • v. t.

    To mark with ruddle; to raddle; to rouge.

  • Bundling
  • p. pr. & vb. n.

    of Bundle

  • Dandle
  • v. t.

    To treat with fondness, as if a child; to fondle; to toy with; to pet.

  • Bungled
  • imp. & p. p.

    of Bungle

  • Furdle
  • v. t.

    To draw up into a bundle; to roll up.

  • Bungler
  • n.

    A clumsy, awkward workman; one who bungles.

  • Buckle
  • n.

    To fasten or confine with a buckle or buckles; as, to buckle a harness.

  • Bundled
  • imp. & p. p.

    of Bundle

  • Unbundle
  • v. t.

    To release, as from a bundle; to disclose.

  • Cuddle
  • v. t.

    To embrace closely; to fondle.

  • Buddle
  • v. i.

    To wash ore in a buddle.

  • Faddle
  • v. t.

    To fondle; to dandle.

  • Bridle
  • v. t.

    To put a bridle upon; to equip with a bridle; as, to bridle a horse.

  • Bundle
  • n.

    A number of things bound together, as by a cord or envelope, into a mass or package convenient for handling or conveyance; a loose package; a roll; as, a bundle of straw or of paper; a bundle of old clothes.

  • Trundle
  • v. t.

    To roll (a thing) on little wheels; as, to trundle a bed or a gun carriage.

  • Bridle
  • v. t.

    To restrain, guide, or govern, with, or as with, a bridle; to check, curb, or control; as, to bridle the passions; to bridle a muse.

  • Curdle
  • v. i.

    To change into curd; to coagulate; as, rennet causes milk to curdle.