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fiber bundle morphism

См. также в других словарях:

  • Bundle map — In mathematics, a bundle map (or bundle morphism) is a morphism in the category of fiber bundles. There are two distinct, but closely related, notions of bundle map, depending on whether the fiber bundles in question have a common base space.… …   Wikipedia

  • Bundle (mathematics) — In mathematics, a bundle is a generalization of a fiber bundle dropping the condition of a local product structure. The requirement of a local product structure rests on the bundle having a topology. Without this requirement, more general objects …   Wikipedia

  • Vector bundle — The Möbius strip is a line bundle over the 1 sphere S1. Locally around every point in S1, it looks like U × R, but the total bundle is different from S1 × R (which is a cylinder instead). In mathematics, a vector bundle is a… …   Wikipedia

  • Pullback bundle — In mathematics, a pullback bundle or induced bundle is a useful construction in the theory of fiber bundles. Given a fiber bundle pi; : E rarr; B and a continuous map f : B prime; rarr; B one can define a pullback of E by f as a bundle f * E over …   Wikipedia

  • Connection (principal bundle) — This article is about connections on principal bundles. See connection (mathematics) for other types of connections in mathematics. In mathematics, a connection is a device that defines a notion of parallel transport on the bundle; that is, a way …   Wikipedia

  • Sheaf (mathematics) — This article is about sheaves on topological spaces. For sheaves on a site see Grothendieck topology and Topos. In mathematics, a sheaf is a tool for systematically tracking locally defined data attached to the open sets of a topological space.… …   Wikipedia

  • Pullback (differential geometry) — Suppose that φ : M → N is a smooth map between smooth manifolds M and N ; then there is an associated linear map from the space of 1 forms on N (the linear space of sections of the cotangent bundle) to the space of 1 forms on M . This linear map… …   Wikipedia

  • Section (category theory) — In category theory, a branch of mathematics, a section (or coretraction) is a right inverse of a morphism. Dually, a retraction (or retract) is a left inverse. In other words, if and are morphisms whose composition is the identity morphism on Y,… …   Wikipedia

  • Pullback (category theory) — In category theory, a branch of mathematics, a pullback (also called a fibered product or Cartesian square) is the limit of a diagram consisting of two morphisms f : X → Z and g : Y → Z with a common codomain. The pullback is often written: P = X …   Wikipedia

  • Fibration — In mathematics, especially algebraic topology, a fibration is a continuous mapping:p:E o B,satisfying the homotopy lifting property with respect to any space. Fiber bundles (over paracompact bases) constitute important examples. In homotopy… …   Wikipedia

  • Descent (category theory) — In mathematics, the idea of descent has come to stand for a very general idea, extending the intuitive idea of gluing in topology. Since the topologists glue is actually the use of equivalence relations on topological spaces, the theory starts… …   Wikipedia

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