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BUNDLE MAP

  • Bundle map
  • mathematics, a bundle map (or bundle morphism) is a function that relates two fiber bundles in a way that respects their internal structure. Fiber bundles are mathematical

    Bundle map

    Bundle_map

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

    In mathematics, a vector bundle is a topological construction that makes precise the idea of a family of vector spaces parameterized by another space X

    Vector bundle

    Vector bundle

    Vector_bundle

  • Fiber bundle
  • Continuous surjection satisfying a local triviality condition

    B.} The map π , {\displaystyle \pi ,} called the projection or submersion of the bundle, is regarded as part of the structure of the bundle. The space

    Fiber bundle

    Fiber bundle

    Fiber_bundle

  • Hopf fibration
  • Fiber bundle of the 3-sphere over the 2-sphere, with 1-spheres as fibers

    differential topology, the Hopf fibration (also known as the Hopf bundle or Hopf map) describes a 3-sphere (a hypersphere in four-dimensional space) in

    Hopf fibration

    Hopf fibration

    Hopf_fibration

  • 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

  • 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

  • Pullback (differential geometry)
  • Mathematical operation

    linear space of sections of the cotangent bundle) to the space of 1-forms on M {\displaystyle M} . This linear map is known as the pullback (by ϕ {\displaystyle

    Pullback (differential geometry)

    Pullback_(differential_geometry)

  • 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

  • Section (fiber bundle)
  • Right inverse of a fiber bundle map

    bundle over a base space, B {\displaystyle B} : π : E → B {\displaystyle \pi \colon E\to B} then a section of that fiber bundle is a continuous map,

    Section (fiber bundle)

    Section (fiber bundle)

    Section_(fiber_bundle)

  • Orientation of a vector bundle
  • Generalization of an orientation of a vector space

    the vector space Ex and one demands that each trivialization map (which is a bundle map) ϕ U : π − 1 ( U ) → U × R n {\displaystyle \phi _{U}:\pi ^{-1}(U)\to

    Orientation of a vector bundle

    Orientation_of_a_vector_bundle

  • Pushforward (differential)
  • Linear approximation of smooth maps on tangent spaces

    obvious manner, a bundle map (in fact a vector bundle homomorphism) from the tangent bundle of M {\displaystyle M} to the tangent bundle of N {\displaystyle

    Pushforward (differential)

    Pushforward (differential)

    Pushforward_(differential)

  • 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

  • Pullback bundle
  • Fiber bundle induced by a map of its base space

    mathematics, a pullback bundle or induced bundle is the fiber bundle that is induced by a map of its base-space. Given a fiber bundle π : E → B {\displaystyle

    Pullback bundle

    Pullback_bundle

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

    disk bundles. It was first described by John Milnor (1956) and subsequently used extensively in surgery theory to produce manifolds and normal maps with

    Plumbing (mathematics)

    Plumbing (mathematics)

    Plumbing_(mathematics)

  • Principal bundle
  • Fiber bundle whose fibers are group torsors

    In the mathematical area of topology, a principal bundle is a mathematical object that formalizes some of the essential features of the Cartesian product

    Principal bundle

    Principal_bundle

  • Universal bundle
  • classifying space BG, such that every bundle with the given structure group G over M is a pullback by means of a continuous map M → BG. When the definition of

    Universal bundle

    Universal_bundle

  • Connection (principal bundle)
  • Concept in mathematics

    transport on the bundle; that is, a way to "connect" or identify fibers over nearby points. A principal G-connection on a principal G-bundle P {\displaystyle

    Connection (principal bundle)

    Connection_(principal_bundle)

  • 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

  • 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

  • Bundle (mathematics)
  • Generalization of a fiber bundle

    and p : E → B is a map. E is called the total space B is the base space of the bundle p is the projection This definition of a bundle is quite unrestrictive

    Bundle (mathematics)

    Bundle_(mathematics)

  • Atlas
  • Collection of maps

    An atlas is a collection of maps; it is typically a bundle of maps of Earth or of a continent or region of Earth. Advances in astronomy have also resulted

    Atlas

    Atlas

    Atlas

  • Quotient stack
  • {\displaystyle P'\to T'} is a bundle map (i.e., forms a commutative diagram) that is compatible with the equivariant maps P → X {\displaystyle P\to X}

    Quotient stack

    Quotient_stack

  • Bundle metric
  • M a vector bundle on M, then a metric on E is a bundle map k : E ×M E → M × R from the fiber product of E with itself to the trivial bundle with fiber

    Bundle metric

    Bundle_metric

  • Differential operator
  • Typically linear operator defined in terms of differentiation of functions

    multi-index α, P α ( x ) : E → F {\displaystyle P^{\alpha }(x):E\to F} is a bundle map, symmetric on the indices α. The kth order coefficients of P transform

    Differential operator

    Differential operator

    Differential_operator

  • Musical isomorphism
  • Isomorphism between the tangent and cotangent bundles of a manifold

    isomorphism) is an isomorphism between the tangent bundle T M {\displaystyle \mathrm {T} M} and the cotangent bundle T ∗ M {\displaystyle \mathrm {T} ^{*}M} of

    Musical isomorphism

    Musical_isomorphism

  • Jet bundle
  • Construction in differential topology

    differential topology, the jet bundle is a certain construction that makes a new smooth fiber bundle out of a given smooth fiber bundle. It makes it possible to

    Jet bundle

    Jet_bundle

  • Clifford module bundle
  • differential geometry, a Clifford module bundle, a bundle of Clifford modules or just Clifford module is a vector bundle whose fibers are Clifford modules,

    Clifford module bundle

    Clifford_module_bundle

  • Equivariant bundle
  • group G (which may be a topological or Lie group), an equivariant bundle is a fiber bundle π : E → B {\displaystyle \pi \colon E\to B} such that the total

    Equivariant bundle

    Equivariant_bundle

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

    holomorphic vector bundle is a complex vector bundle over a complex manifold X such that the total space E is a complex manifold and the projection map π : E → X

    Holomorphic vector bundle

    Holomorphic_vector_bundle

  • Pullback (category theory)
  • Most general completion of a commutative square given two morphisms with same codomain

    bundles: given a bundle map π : E → B and a continuous map f : X → B, the pullback (formed in the category of topological spaces with continuous maps)

    Pullback (category theory)

    Pullback_(category_theory)

  • Spin structure
  • Concept in differential geometry

    PSO(E) to a principal bundle PSpin(E) under the action of the spin group Spin(n), by which we mean that there exists a bundle map ϕ {\displaystyle \phi

    Spin structure

    Spin_structure

  • Ample line bundle
  • Concept in algebraic geometry

    an ample line bundle, although there are several related classes of line bundles. Roughly speaking, positivity properties of a line bundle are related to

    Ample line bundle

    Ample_line_bundle

  • 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

  • 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

  • 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)

  • Stiefel–Whitney class
  • Set of topological invariants

    of a real vector bundle that describe the obstructions to constructing everywhere independent sets of sections of the vector bundle. Stiefel–Whitney classes

    Stiefel–Whitney class

    Stiefel–Whitney_class

  • Integral curve
  • Term in mathematics

    of induced maps. Note that the tangent bundle TJ of J is the trivial bundle J × R and there is a canonical cross-section ι of this bundle such that ι(t)

    Integral curve

    Integral_curve

  • Circle bundle
  • Principal fiber bundle

    bundle is a fiber bundle where the fiber is the circle S 1 {\displaystyle S^{1}} . Oriented circle bundles are also known as principal U(1)-bundles,

    Circle bundle

    Circle_bundle

  • Solder form
  • Mathematical construct of fiber bundles

    representation V of G such that the associated bundle map from the tangent bundle TM to the associated bundle P×G V is a bundle isomorphism. (In particular, V and

    Solder form

    Solder form

    Solder_form

  • Complex projective space
  • Mathematical concept

    complex line bundles. Equivalently it accounts for the first Chern class. This can be seen heuristically by looking at the fiber bundle maps S 1 ↪ S 2 n

    Complex projective space

    Complex projective space

    Complex_projective_space

  • Gauss map
  • Differential geometry topic

    tangent bundle TM. In the case where M = R n {\displaystyle M=\mathbf {R} ^{n}} , the tangent bundle is trivialized (so the Grassmann bundle becomes a map to

    Gauss map

    Gauss_map

  • G-structure on a manifold
  • Structure group sub-bundle on a tangent frame bundle

    the structure group of a G-bundle B is choosing an H-bundle whose image is B. The inducing map from H-bundles to G-bundles is in general neither onto

    G-structure on a manifold

    G-structure_on_a_manifold

  • Contact bundle
  • Bundle of linear subspaces of the tangent bundle

    geometry, a contact bundle is a particular type of fiber bundle constructed from a smooth manifold. Like how the tangent bundle is the manifold that

    Contact bundle

    Contact_bundle

  • Piri Reis map
  • 1513 Ottoman nautical chart

    search for potentially overlooked maps. Halil Edhem found a disregarded bundle of material containing an unusual parchment map. They showed the parchment to

    Piri Reis map

    Piri Reis map

    Piri_Reis_map

  • Lie algebroid
  • Infinitesimal version of Lie groupoid

    groupoid gives rise to a Lie algebroid, which is the vertical bundle of the source map restricted at the units. However, unlike Lie algebras, not every

    Lie algebroid

    Lie_algebroid

  • 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

  • Gysin homomorphism
  • Long exact sequence

    sequence. Consider a fiber-oriented sphere bundle with total space E, base space M, fiber Sk and projection map π {\displaystyle \pi } : S k ↪ E ⟶ π M .

    Gysin homomorphism

    Gysin_homomorphism

  • Tensor field
  • Assignment of a tensor continuously varying across a region of space

    cotangent space. See also tangent bundle and cotangent bundle. Given two tensor bundles E → M and F → M, a linear map A: Γ(E) → Γ(F) from the space of

    Tensor field

    Tensor field

    Tensor_field

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

    new charts is the tangent bundle for the charts Uα. The transition maps on this atlas are defined from the transition maps on the original manifold, and

    Differentiable manifold

    Differentiable manifold

    Differentiable_manifold

  • Coherent sheaf
  • Generalization of vector bundles

    Coherent sheaves can be seen as a generalization of vector bundles. Unlike vector bundles, they form an abelian category, and so they are closed under

    Coherent sheaf

    Coherent_sheaf

  • Double tangent bundle
  • double tangent bundle or the second tangent bundle refers to the tangent bundle (TTM,πTTM,TM) of the total space TM of the tangent bundle (TM,πTM,M) of

    Double tangent bundle

    Double_tangent_bundle

  • 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

  • Dual abelian variety
  • data of a map f ∨ : B ∨ → A ∨ {\displaystyle f^{\vee }:B^{\vee }\to A^{\vee }} is the same as giving a family of degree zero line bundles on A {\displaystyle

    Dual abelian variety

    Dual_abelian_variety

  • Glossary of algebraic geometry
  • a vector-bundle map f : E → F {\displaystyle f:E\to F} over a variety X (that is, a scheme X-morphism between the total spaces of the bundles), the degeneracy

    Glossary of algebraic geometry

    Glossary_of_algebraic_geometry

  • 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

  • Associated bundle
  • Fiber bundle

    theory of fiber bundles with a structure group G {\displaystyle G} (a topological group) allows an operation of creating an associated bundle, in which the

    Associated bundle

    Associated_bundle

  • Banach bundle
  • Concept in mathematics

    In mathematics, a Banach bundle is a vector bundle each of whose fibres is a Banach space, i.e. a complete normed vector space, possibly of infinite dimension

    Banach bundle

    Banach_bundle

  • Tubular neighborhood
  • Neighborhood of a submanifold

    the normal bundle of S in M. Here S plays the role of the curve and M the role of the plane containing the curve. Consider the natural map i : N 0 → S

    Tubular neighborhood

    Tubular neighborhood

    Tubular_neighborhood

  • Affine connection
  • Construct allowing differentiation of tangent vector fields of manifolds

    ω on the frame bundle FM or GL(M) of a manifold M. In more detail, ω is a smooth map from the tangent bundle T(FM) of the frame bundle to the space of

    Affine connection

    Affine connection

    Affine_connection

  • Euler class
  • Characteristic class of oriented, real vector bundles

    real vector bundles. Like other characteristic classes, it measures how "twisted" the vector bundle is. In the case of the tangent bundle of a smooth

    Euler class

    Euler_class

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

    theory is the general study of connections on vector bundles, principal bundles, and fibre bundles. Gauge theory in mathematics should not be confused

    Gauge theory (mathematics)

    Gauge_theory_(mathematics)

  • 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

  • Dual bundle
  • Mathematical operation on vector bundles

    the dual bundle is an operation on vector bundles extending the operation of duality for vector spaces. The dual bundle of a vector bundle π : E → X

    Dual bundle

    Dual_bundle

  • Secondary vector bundle structure
  • Mathematical concept in particularly differential topology

    vector bundle structure refers to the natural vector bundle structure (TE, p∗, TM) on the total space TE of the tangent bundle of a smooth vector bundle (E

    Secondary vector bundle structure

    Secondary_vector_bundle_structure

  • Splitting principle
  • Mathematical technique for vector bundles

    ( E ) {\displaystyle Y=Fl(E)} , called the flag bundle associated to E {\displaystyle E} , and a map p : Y → X {\displaystyle p\colon Y\rightarrow X}

    Splitting principle

    Splitting_principle

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

    \operatorname {SU} (2)} -bundles (or principal Sp ⁡ ( 1 ) {\displaystyle \operatorname {Sp} (1)} -bundles) are special principal bundles with the second special

    Principal SU(2)-bundle

    Principal_SU(2)-bundle

  • Anosov diffeomorphism
  • Diffeomorphism that has a hyperbolic structure on the tangent bundle

    differentiable map f on M has a hyperbolic structure on the tangent bundle, then it is called an Anosov map. Examples include the Bernoulli map, and Arnold's

    Anosov diffeomorphism

    Anosov_diffeomorphism

  • Indifference curve
  • Concept in economics

    consumption bundles by order of preference. A graph of indifference curves for several utility levels of an individual consumer is called an indifference map. Points

    Indifference curve

    Indifference curve

    Indifference_curve

  • Vector-valued differential form
  • V. More generally, it is a differential form with values in some vector bundle E over M. Ordinary differential forms can be viewed as R-valued differential

    Vector-valued differential form

    Vector-valued_differential_form

  • Natural bundle
  • geometry, a field in mathematics, a natural bundle is any fiber bundle associated to the higher order frame bundle F r ( M ) {\displaystyle F^{r}(M)} , for

    Natural bundle

    Natural_bundle

  • 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 bundles with a structure group from a given base space, fiber

    Fiber bundle construction theorem

    Fiber bundle construction theorem

    Fiber_bundle_construction_theorem

  • Tensor bundle
  • Concept in mathematics

    mathematics, the tensor bundle of a manifold is the direct sum of all tensor products of the tangent bundle and the cotangent bundle of that manifold. To

    Tensor bundle

    Tensor_bundle

  • Normal invariant
  • Concept in geometric topology

    has a good candidate for a stable normal bundle and a Thom collapse map, which is equivalent to there being a map from a manifold M to X matching the fundamental

    Normal invariant

    Normal_invariant

  • Torus bundle
  • {\displaystyle f} is the identity map (i.e., the map which fixes every point of the torus) then the resulting torus bundle M ( f ) {\displaystyle M(f)} is

    Torus bundle

    Torus_bundle

  • Homotopy lifting property
  • Homotopy theory in algebraic topology

    the projection in a vector bundle, fiber bundle or fibration, where there need be no unique way of lifting. Assume all maps are continuous functions between

    Homotopy lifting property

    Homotopy lifting property

    Homotopy_lifting_property

  • Birational geometry
  • Field of algebraic geometry

    is again a line bundle. For d ≥ 0, the vector space of global sections H0(X, KXd) has the remarkable property that a birational map f : X ⇢ Y between

    Birational geometry

    Birational geometry

    Birational_geometry

  • Immersion (mathematics)
  • Differentiable function whose derivative is everywhere injective

    codimension 0 immersion of a closed manifold is precisely a covering map, i.e., a fiber bundle with 0-dimensional (discrete) fiber. By Ehresmann's theorem and

    Immersion (mathematics)

    Immersion (mathematics)

    Immersion_(mathematics)

  • Homotopy
  • Continuous deformation between two continuous functions

    ^{n}-\{0\}\to S^{n-1}} is a fiber bundle with fiber R > 0 {\displaystyle \mathbb {R} _{>0}} . Every vector bundle is a fiber bundle with a fiber homotopy equivalent

    Homotopy

    Homotopy

    Homotopy

  • List of differential geometry topics
  • Fiber bundle Principal bundle Frame bundle Hopf bundle Associated bundle Vector bundle Tangent bundle Cotangent bundle Line bundle Jet bundle Sheaf (mathematics)

    List of differential geometry topics

    List_of_differential_geometry_topics

  • Ehresmann connection
  • Differential geometry construct on fiber bundles

    on any smooth fiber bundle. In particular, it does not rely on the possible vector bundle structure of the underlying fiber bundle, but nevertheless, linear

    Ehresmann connection

    Ehresmann_connection

  • Surgery exact sequence
  • Tool to classify manifolds within a homotopy type in dim > 4

    from the stable tangent bundle of M {\displaystyle M} to some bundle ξ {\displaystyle \xi } over X {\displaystyle X} . Two such maps are equivalent if there

    Surgery exact sequence

    Surgery_exact_sequence

  • Classifying space for U(n)
  • Exact homotopy case

    together with a universal bundle EU(n) such that any hermitian bundle on a paracompact space X is the pull-back of EU(n) by a map X → BU(n) unique up to

    Classifying space for U(n)

    Classifying_space_for_U(n)

  • Iitaka dimension
  • the Iitaka dimension of a line bundle L on an algebraic variety X is the dimension of the image of the rational map to projective space determined by

    Iitaka dimension

    Iitaka_dimension

  • 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

  • Theatrum Orbis Terrarum
  • 1570 atlas by Abraham Ortelius

    virtually no maps from the hand of Ortelius, but 53 bundled maps of other masters, with the source as indicated. Previously, groupings of disparate maps were

    Theatrum Orbis Terrarum

    Theatrum Orbis Terrarum

    Theatrum_Orbis_Terrarum

  • Clutching construction
  • Topological construct

    trivialized fiber bundles with fiber F {\displaystyle F} and structure group G {\displaystyle G} over the two hemispheres, then given a map f : S n − 1 →

    Clutching construction

    Clutching_construction

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

    needed relates to the elliptic complex of vector bundles E j {\displaystyle E_{j}} , namely a bundle map φ j : f − 1 ( E j ) → E j {\displaystyle \varphi

    Atiyah–Bott fixed-point theorem

    Atiyah–Bott_fixed-point_theorem

  • Cartan connection
  • Generalization of affine connections

    concept of a principal connection, in which the geometry of the principal bundle is tied to the geometry of the base manifold using a solder form. Cartan

    Cartan connection

    Cartan_connection

  • Exterior covariant derivative
  • Concept in differential geometry

    differentiable principal bundle or vector bundle with a connection. Let G be a Lie group and P → M be a principal G-bundle on a smooth manifold M. Suppose

    Exterior covariant derivative

    Exterior_covariant_derivative

  • Chern class
  • Characteristic classes of vector bundles

    vector bundle to a classifying space (an infinite Grassmannian in this case). For any complex vector bundle V over a manifold M, there exists a map f from

    Chern class

    Chern_class

  • Conic bundle
  • In algebraic geometry, a conic bundle is an algebraic variety that appears as a solution to a Cartesian equation of the form: X 2 + a X Y + b Y 2 = P (

    Conic bundle

    Conic_bundle

  • Shriek map
  • Exceptional functor

    fiber bundles, where they yield maps that have the opposite of the usual variance. They are thus called wrong way maps, umkehr maps, Gysin maps, as they

    Shriek map

    Shriek_map

  • Holonomy
  • Concept in differential geometry

    projection map, is a principal bundle over M with structure group Hol p ⁡ ( ω ) . {\displaystyle \operatorname {Hol} _{p}(\omega ).} This principal bundle is

    Holonomy

    Holonomy

    Holonomy

  • List of The Joey Bishop Show episodes
  • baby's arrival Joey tries to appear calm and cool, but in reality he's a bundle of nerves. The Doctor (Frank Wilcox) checks in on Ellie and tells Joey she

    List of The Joey Bishop Show episodes

    List_of_The_Joey_Bishop_Show_episodes

  • Category (mathematics)
  • Mathematical object that generalizes the standard notions of sets and functions

    of concrete categories are given by the following table. Fiber bundles with bundle maps between them form a concrete category. The category Cat consists

    Category (mathematics)

    Category (mathematics)

    Category_(mathematics)

  • Affine bundle
  • Type of fiber bundle

    In mathematics, an affine bundle is a fiber bundle whose typical fiber, fibers, trivialization morphisms and transition functions are affine. Let π ¯ :

    Affine bundle

    Affine_bundle

  • Metric connection
  • Construct in differenital geometry

    mathematics, a metric connection is a connection in a vector bundle E equipped with a bundle metric; that is, a metric for which the inner product of any

    Metric connection

    Metric_connection

  • Courant algebroid
  • Concept in differential geometry

    \langle \cdot ,\cdot \rangle :E\times E\to M\times \mathbb {R} } , and a bundle map ρ : E → T M {\displaystyle \rho :E\to TM} (called anchor) subject to the

    Courant algebroid

    Courant_algebroid

  • Vector space
  • Algebraic structure in linear algebra

    map π : E → X {\displaystyle \pi :E\to X} such that for every x in X, the fiber π−1(x) is a vector space. The case dim V = 1 is called a line bundle.

    Vector space

    Vector space

    Vector_space

  • Atlas (topology)
  • Set of charts that describes a manifold

    the transition maps between charts of an atlas preserve a local trivialization, then the atlas defines the structure of a fibre bundle. Smooth atlas Smooth

    Atlas (topology)

    Atlas_(topology)

AI & ChatGPT searchs for online references containing BUNDLE MAP

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BUNDLE MAP

  • 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

  • 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

  • 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

  • Yandle
  • Surname or Lastname

    English

    Yandle

    English : variant of Yandell.

    Yandle

  • 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

  • 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

  • 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

  • Huddle
  • Surname or Lastname

    English

    Huddle

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

    Huddle

  • 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

  • Hundley
  • Surname or Lastname

    English (Worcestershire)

    Hundley

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

    Hundley

  • 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

  • Beedle
  • Surname or Lastname

    English

    Beedle

    English : variant spelling of Beadle.

    Beedle

  • Durapa
  • Boy/Male

    Indian

    Durapa

    Bundle of Joy

    Durapa

  • Kindle
  • Surname or Lastname

    English

    Kindle

    English : variant of Kendall.Variant of German Kindel.

    Kindle

  • Hurdle
  • Surname or Lastname

    English

    Hurdle

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

    Hurdle

  • 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

  • Bunte
  • Surname or Lastname

    German (Bünte)

    Bunte

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

    Bunte

  • 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

  • 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

  • Rundle
  • Surname or Lastname

    English

    Rundle

    English : variant of Rundell.Respelling of German Rundel.

    Rundle

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  • Ruddle
  • v. t.

    To mark with ruddle; to raddle; to rouge.

  • Bridle
  • v. t.

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

  • Buckle
  • n.

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

  • Bundling
  • p. pr. & vb. n.

    of Bundle

  • Bungler
  • n.

    A clumsy, awkward workman; one who bungles.

  • 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.

  • Bungled
  • imp. & p. p.

    of Bungle

  • Bundle
  • v. t.

    To tie or bind in a bundle or roll.

  • Dandle
  • v. t.

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

  • 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.

  • Bundled
  • imp. & p. p.

    of Bundle

  • Unbundle
  • v. t.

    To release, as from a bundle; to disclose.

  • 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.

  • Buddle
  • v. i.

    To wash ore in a buddle.

  • Faddle
  • v. t.

    To fondle; to dandle.

  • Puddle
  • v. t.

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

  • Trundle
  • v. t.

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

  • Cuddle
  • v. t.

    To embrace closely; to fondle.

  • Furdle
  • v. t.

    To draw up into a bundle; to roll up.

  • Curdle
  • v. i.

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