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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
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
Concept in mathematics
any fiber bundle associated to P {\displaystyle P} via the associated bundle construction. In particular, on any associated vector bundle the principal
Connection_(principal_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
Constructs a fiber bundle from a base space, fiber and a set of transition functions
which two such bundles are isomorphic. The theorem is used in the associated bundle construction, where one starts with a given bundle and changes just
Fiber bundle construction theorem
Fiber_bundle_construction_theorem
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)
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
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
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)
Principal bundle formulation of the Higgs field
some composite bundle E → P / H → X {\displaystyle E\to P/H\to X} , where E → P / H {\displaystyle E\to P/H} is some associated bundle to P → P / H {\displaystyle
Higgs_field_(classical)
Topics referred to by the same term
Look up bundle in Wiktionary, the free dictionary. Bundle or Bundling may refer to: Bundling (packaging), the process of using straps to bundle up items
Bundle
geometry, a stable principal bundle is a generalisation of the notion of a stable vector bundle to the setting of principal bundles. The concept of stability
Stable_principal_bundle
There is a natural Clifford bundle associated to any (pseudo) Riemannian manifold M which is called the Clifford bundle of M. This is commonly referred
Clifford_bundle
Digital storefront company selling video games and e-books
Humble Bundle, Inc. is a digital storefront for video games, which grew out of its original offering of Humble Bundles, collections of games sold at a
Humble_Bundle
mathematics, an adjoint bundle is a vector bundle naturally associated with any smooth principal bundle. The fibers of the adjoint bundle carry a Lie algebra
Adjoint_bundle
the conformal group (see associated bundle). The term tractor is a portmanteau of "Tracy Thomas" and "twistor", the bundle having been introduced first
Tractor_bundle
Construction in differential topology
phenomena associated with the derivatives of maps, particularly those associated with the calculus of variations. Consequently, the jet bundle is now recognized
Jet_bundle
Section of a certain line bundle
a density is a section of a certain line bundle, called the density bundle. An element of the density bundle at x is a function that assigns a volume
Density_on_a_manifold
algebra bundle is a vector bundle. Examples include the tensor-algebra bundle, exterior bundle, and symmetric bundle associated to a given vector bundle, as
Algebra_bundle
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
Mathematical operation on vector bundles
bundle of an associated bundle is the bundle associated to the dual representation of the structure group. The dual bundle of the tangent bundle of a differentiable
Dual_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
Courting behavior
especially in Pennsylvania Dutch Country. Bundling is associated with the Amish as a form of courtship. Bundling, or "bed courting", is believed to have
Bundling_(tradition)
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
Concept in mathematics
the associated bundle construction. The Borel–Weil–Bott theorem says that all representations of G arise as the cohomologies of such line bundles. If
Equivariant_sheaf
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,
Solder_form
Structure group sub-bundle on a tangent frame bundle
H} -bundle Q {\displaystyle Q} and an isomorphism ϕ Q : Q × H G → P {\displaystyle \phi _{Q}\colon Q\times _{H}G\to P} of the associated bundle to the
G-structure_on_a_manifold
Possibility of a consistent definition of "clockwise" in a mathematical space
\operatorname {O} (M)} is the bundle of pseudo-orthogonal frames. Similarly, a time orientation is a section of the associated bundle O ( M ) × σ − { − 1
Orientability
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
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
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
be extended to an arbitrary vector bundle, and to some principal fiber bundles. This metric is often called a bundle metric, or fibre metric. If M is a
Bundle_metric
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
Topics referred to by the same term
Software bundle may refer to: Pre-installed software Bundled software Software suite Solution stack This disambiguation page lists articles associated with
Software_bundle
Heart block in the right ventricle
RBBB with associated first degree AV block RBBB with associated tachycardia RBBB Bundle branch block Intraventricular block Left bundle branch block
Right_bundle_branch_block
Mathematical operation
there is an associated linear map from the space of 1-forms on N {\displaystyle N} (the linear space of sections of the cotangent bundle) to the space
Pullback (differential geometry)
Pullback_(differential_geometry)
Topics referred to by the same term
JavaScript development. webpack, module bundler This disambiguation page lists articles associated with the title Bundler. If an internal link incorrectly led
Bundler
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
Geometric structure
the spinor bundle to be the complex vector bundle π S : S → M {\displaystyle \pi _{\mathbf {S} }\colon {\mathbf {S} }\to M\,} associated to the corresponding
Spinor_bundle
Offering several products as one
In marketing, product bundling is offering several products or services for sale as one combined product or service package. It is a common feature in
Product_bundling
Vector bundle associated with conformal manifolds
differential geometry, the local twistor bundle is a specific vector bundle with connection that can be associated to any conformal manifold, at least locally
Local_twistor
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
on the frame bundle of a manifold or the induced connection on any associated bundle — such a connection is equivalently given by a Cartan connection for
Linear_connection
Construct allowing differentiation of tangent vector fields of manifolds
which induces a bundle homomorphism from TM to the associated bundle P ×GL(n) Rn. Condition 3 is equivalent to the fact that this bundle homomorphism is
Affine_connection
have important applications in the theory of connections on a principal bundle as well as in the theory of Cartan connections. A Lie-algebra-valued differential
Lie algebra–valued differential form
Lie_algebra–valued_differential_form
Type of fiber bundle on a Riemann surface
indigenous bundle on a Riemann surface is a fiber bundle with a flat connection associated to some complex projective structure. Indigenous bundles were introduced
Indigenous_bundle
Mathematical concept that extends the intuitive idea of gluing in topology
implies a vector bundle on Y (so, a bundle given on each Xi), and our concern is to 'glue' those bundles Vi, to make a single bundle V on X. What we mean
Descent_(mathematics)
mathematics, the universal bundle in the theory of fiber bundles with structure group a given topological group G, is a specific bundle over a classifying space
Universal_bundle
Restriction of electrical impulse flow in the heart's bundle branches
A bundle branch block is a partial or complete interruption in the flow of electrical impulses in either of the bundle branches of the heart's electrical
Bundle_branch_block
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
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
mathematics, a monopole is a connection over a principal bundle G with a section of the associated adjoint bundle. Physically, such a monopole can be interpreted
Monopole_(mathematics)
Derivative used in gauge theories
an associated bundle for the principal fiber bundle of the gauge theory; and, for the case of spinors, the associated bundle would be a spin bundle of
Gauge_covariant_derivative
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
Acronym for a common web hosting solution
Computertechnik, a German computing magazine, as he demonstrated that a bundle of free and open-source software "could be a feasible alternative to expensive
LAMP_(software_bundle)
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
In the brain, the angular bundle is a composite fiber tract within the ventrolateral aspect of the lateral ventricle's temporal horn. It contains the perforant
Angular_bundle
Atiyah algebroid, or Atiyah sequence, of a principal G {\displaystyle G} -bundle P {\displaystyle P} over a manifold M {\displaystyle M} , where G {\displaystyle
Atiyah_algebroid
vector bundle is a (holomorphic or algebraic) vector bundle that is stable in the sense of geometric invariant theory. Any holomorphic vector bundle may
Stable_vector_bundle
{\textstyle \mathrm {U} (n)} and the associated bundle construction. Indeed, the ω {\textstyle \omega } -symplectic frame bundle P S p → M {\textstyle P_{\mathrm
Almost_symplectic_manifold
Way to create new manifolds out of disk bundles
D ( E i ) {\displaystyle D(E_{i})} the total space of the associated (closed) disk bundle D ( ξ i ) {\displaystyle D(\xi _{i})} and suppose that ξ i
Plumbing_(mathematics)
French mathematician (1914–1945)
written together with Ehresmann, he introduced the notion of an associated bundle and proved results known today as the exact homotopy sequence of a
Jacques_Feldbau
Category of cloud computing
a modular bundle of a computing platform and applications, without the complexity of building and maintaining the infrastructure associated with developing
Platform_as_a_service
Concept in differential geometry
an orientable Riemannian manifold (M, g) allows one to define associated spinor bundles, giving rise to the notion of a spinor in differential geometry
Spin_structure
Type of differentiable manifold
{\displaystyle p} . Equivalently, the tangent bundle is a trivial bundle, so that the associated principal bundle of linear frames has a global section on
Parallelizable_manifold
Algebraic topology uses abstract algebra to study topological spaces
Eilenberg–MacLane space Fibre bundle Möbius strip Line bundle Canonical line bundle Vector bundle Associated bundle Fibration Hopf bundle Classifying space Cofibration
List of algebraic topology topics
List_of_algebraic_topology_topics
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
\operatorname {Pic} ^{0}(A)} is called a degree 0 line bundle on A. To A one then associates a dual abelian variety Av (over the same field), which is
Dual_abelian_variety
Scheme parametrizing flags in the fibers of a vector bundle
<d_{r}<n.} The flag bundle, or relative flag variety, of type ( d 1 , … , d r ) {\displaystyle (d_{1},\ldots ,d_{r})} associated with E {\displaystyle
Flag_bundle
Correspondsnce between Higgs bundles and fundamental group representations
structure group π 1 ( X ) {\displaystyle \pi _{1}(X)} . Thus there is an associated bundle to X ^ {\displaystyle {\hat {X}}} given by E = X ^ × ρ C r . {\displaystyle
Nonabelian Hodge correspondence
Nonabelian_Hodge_correspondence
Mathematical transformation
π : E → M {\textstyle \pi :E\to M} be a vector bundle on M {\displaystyle M} and its associated bundle projection, respectively. Let L : E → R {\textstyle
Legendre_transformation
Principle in the philosophy of science
concepts. In recent decades, the set of associated assumptions supporting a thesis sometimes is called a bundle of hypotheses, i.e. a hypothesis and its
Duhem–Quine_thesis
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
Topological space associated to a vector bundle
algebraic topology and differential topology is a topological space associated to a vector bundle, over any paracompact space. One way to construct this space
Thom_space
Conic bundles can be considered as either a Severi–Brauer or Châtelet surface. This can be a double covering of a ruled surface. It can be associated with
Conic_bundle
In mathematics, a bundle gerbe is a geometrical model of certain 1-gerbes with connection, or equivalently of a 2-class in Deligne cohomology. U ( 1 )
Bundle_gerbe
Mathematical technique for vector bundles
exists a space Y = F l ( E ) {\displaystyle Y=Fl(E)} , called the flag bundle associated to E {\displaystyle E} , and a map p : Y → X {\displaystyle p\colon
Splitting_principle
is a principal bundle with a structure group H {\displaystyle H} and P / H → X {\displaystyle P/H\to X} is a fiber bundle associated with P → X {\displaystyle
Connection_(composite_bundle)
Topological space
of circles. In other words, it is a S 1 {\displaystyle S^{1}} -bundle (circle bundle) over a 2-dimensional orbifold. Many 3-manifolds are Seifert fiber
Seifert_fiber_space
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
Fiber bundle of the 3-sphere over the 2-sphere, with 1-spheres as fibers
In differential topology, the Hopf fibration (also known as the Hopf bundle or Hopf map) describes a 3-sphere (a hypersphere in four-dimensional space)
Hopf_fibration
Metric on a determinant line bundle
compute the holonomy of certain determinant line bundles of Dirac operators, and this holonomy is associated to certain anomaly cancellations in Chern–Simons
Quillen_metric
Long exact sequence
of a sphere bundle. The Gysin sequence is a useful tool for calculating the cohomology rings given the Euler class of the sphere bundle and vice versa
Gysin_homomorphism
connection ∇ {\displaystyle \nabla } is a connection on a Hermitian vector bundle E {\displaystyle E} over a smooth manifold M {\displaystyle M} which is
Hermitian_connection
bundle of a Riemannian manifold (M, g), denoted by T1M, UT(M), UTM, or SM is the unit sphere bundle for the tangent bundle T(M). It is a fiber bundle
Unit_tangent_bundle
bundle modelled over a vector bundle Y → X. A connection Γ on Y → X is called the affine connection if it as a section Γ : Y → J1Y of the jet bundle J1Y
Connection_(affine_bundle)
Hermite–Einstein connection) is a Chern connection associated to an inner product on a holomorphic vector bundle over a Kähler manifold that satisfies an analogue
Hermitian Yang–Mills connection
Hermitian_Yang–Mills_connection
Classical field theories on fiber bundles
remove this subtlety. An associated vector bundle E → π M {\displaystyle E\xrightarrow {\pi } M} associated to the principal bundle P {\displaystyle P} through
Covariant classical field theory
Covariant_classical_field_theory
Set of topological invariants
-characteristic class associated to real vector bundles. In algebraic geometry one can also define analogous Stiefel–Whitney classes for vector bundles with a non-degenerate
Stiefel–Whitney_class
Abnormal heart rhythm due to faulty electrical connections in the heart
death.[citation needed] WPW may be associated with PRKAG2, a protein kinase enzyme encoded by the PRKAG2 gene. The bundle of Kent is an abnormal extra or
Wolff–Parkinson–White syndrome
Wolff–Parkinson–White_syndrome
Ruled surface over the projective line
{\displaystyle \mathbb {P} ^{1}} -bundle (a projective bundle) over the projective line P 1 {\displaystyle \mathbb {P} ^{1}} , associated to the sheaf O ⊕ O ( −
Hirzebruch_surface
Location that is mentioned in several of the Mesoamerican codices
Mesoamerica scholars as 'Red and White Bundle' derives from the appearance of the toponymic glyph associated with it in the pictorial Mixtec codices
Red_and_White_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
In mathematics, a vector bundle is said to be flat if it is endowed with a linear connection with vanishing curvature, i.e. a flat connection. Let π :
Flat_vector_bundle
sequence motif associated with three-helix bundles, so they cannot necessarily be predicted from sequence alone. Three-helix bundles often occur in actin-binding
Helix_bundle
Application of topology
metric and an associated space-time structure is a space-time. Gravitation theory is formulated as classical field theory on natural bundles over a world
World_manifold
Mathematics glossary
sense: every local coefficient system over B can be given as the associated bundle B ~ × π 1 B A {\displaystyle {\widetilde {B}}\times _{\pi _{1}B}A}
Glossary of algebraic topology
Glossary_of_algebraic_topology
Math/physics concept
through the gauge covariant derivative. A connection form associates to each basis of a vector bundle a matrix of differential forms. The connection form is
Connection_form
Type of surface in algebraic geometry
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
Bound bundle of wooden rods, sometimes with an axe
plurale tantum, from the Latin word fascis, meaning 'bundle'; Italian: fascio littorio) is a bound bundle of wooden rods, often, but not always, including
Fasces
ASSOCIATED BUNDLE
ASSOCIATED BUNDLE
Boy/Male
Indian
Is associated to Lord Ayyappa
Girl/Female
Arabic, Muslim
Associate; Table Companion
Girl/Female
Tamil
Is associated to Lord Ayyappa
Boy/Male
Hindu
Is associated to Lord Ayyappa
Girl/Female
Indian
Is associated to Goddess Durga
Boy/Male
Hindu
Is associated to Lord Ayyappa
Girl/Female
Sikh
Associated, Connected
Boy/Male
Biblical American Hebrew
Associated with him.
Girl/Female
Tamil
Is associated to Lord Vishnu
Boy/Male
Hindu, Indian, Traditional
Lord Chaitanya's Associate
Boy/Male
Muslim
Associate
Boy/Male
Arabic, Muslim, Sindhi
Associate
Boy/Male
Muslim/Islamic
Associate
Girl/Female
Tamil
Is associated to God Murugan
Girl/Female
Tamil
Is associated to God Murugan
Boy/Male
Indian
Associated with faithfulness
Boy/Male
Arabic
Table Companion; Associate
Girl/Female
Hindu
Is associated to God Murugan
Boy/Male
Muslim
Table companion. Associate.
Boy/Male
Muslim
Associated with faithfulness
ASSOCIATED BUNDLE
ASSOCIATED BUNDLE
Boy/Male
Tamil
Girl/Female
Tamil
Suravinda | ஸà¯à®°à®µà®¿à®¨à¯à®¤à®¾
Beautiful yaksa
Boy/Male
British, English
From the Priest's Meadow
Boy/Male
Australian, Finnish
Son
Girl/Female
Tamil
Abhirami | அபிராமீ
Goddess Parvati, Goddess Lakshmi
Boy/Male
Hindu
The nilgiris, Blue mountain
Surname or Lastname
English
English : variant of Boggs.Lithuanian : respelling of Polish Bogusz or shortened form of the Lithuanian family names BoguÅ¡as, BoguÅ¡a, BoguÅ¡auskas, or BoguseviÄius, all derivatives of Bogusz.
Female
Japanese
(1-明, 2-亮) Japanese unisex name AKIRA means 1) "bright" or 2) "clear."
Girl/Female
Greek American
Most beautiful. Calista was a Mythological Arcadian who transformed into a she-bear, then into...
Boy/Male
Hindu, Indian, Kashmiri
Wind; Victory
ASSOCIATED BUNDLE
ASSOCIATED BUNDLE
ASSOCIATED BUNDLE
ASSOCIATED BUNDLE
ASSOCIATED BUNDLE
a.
Connected by habit or sympathy; as, associate motions, such as occur sympathetically, in consequence of preceding motions.
v. t.
To join or connect; to combine in acting; as, particles of gold associated with other substances.
a.
Not /ell associated or assorted; incongruous.
v. i.
To associate.
n.
One who customarily associates with another; a companion; an associate; any object which is associated or combined with a similar object.
v. i.
To associate.
n.
One connected with an association or institution without the full rights or privileges of a regular member; as, an associate of the Royal Academy.
a.
Joined; associated; coupled.
a.
Closely connected or joined with some other, as in interest, purpose, employment, or office; sharing responsibility or authority; as, an associate judge.
p. pr. & vb. n.
of Associate
a.
Associated.
n.
An associate.
n.
An associate; a confederate or partner in any scheme.
v. i.
To unite in company; to keep company, implying intimacy; as, congenial minds are disposed to associate.
a.
United; connected; associated.
v. t.
To join with one, as a friend, companion, partner, or confederate; as, to associate others with us in business, or in an enterprise.
a.
Joined as a companion; brought into association; accompanying; combined.
a.
Admitted to some, but not to all, rights and privileges; as, an associate member.
a.
Wrongly allied or associated.
imp. & p. p.
of Associate