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

the mathematical field of topology, a section (or cross section) of a fiber bundle E {\displaystyle E} is a continuous right inverse of the projection function...

its optical waveguide properties. Individual coated fibers (or fibers formed into ribbons or bundles) then have a tough resin buffer layer or core tube(s)...

A principal G {\displaystyle G} -bundle, where G {\displaystyle G} denotes any topological group, is a fiber bundle π : P → X {\displaystyle \pi :P\to...

its tangent bundle is trivial. Vector bundles are almost always required to be locally trivial, which means they are examples of fiber bundles. Also, the...

In mathematics, the fiber bundle construction theorem is a theorem which constructs a fiber bundle from a given base space, fiber and a suitable set of...

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

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...

Discovered by Heinz Hopf in 1931, it is an influential early example of a fiber bundle. Technically, Hopf found a many-to-one continuous function (or "map")...

each fiber, we get a line bundle on P ( V ) {\displaystyle \mathbf {P} (V)} . This line bundle is called the tautological line bundle. This line bundle is...

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

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

to a manifold is the prototypical example of a vector bundle (which is a fiber bundle whose fibers are vector spaces). A section of T M {\displaystyle TM}...

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...

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 fibers over nearby...

maps) X ×B E is a fiber bundle over X called the pullback bundle. The associated commutative diagram is a morphism of fiber bundles. A special case is...

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...

A fiberscope is a flexible optical fiber bundle with a lens on one end and an eyepiece or camera on the other. It is used to examine and inspect small...

smooth (Hausdorff) manifold turning G into a fiber bundle with fiber H and base G/H. This fiber bundle is actually principal, with structure group H...

giving a fiber bundle p : M π → X {\displaystyle p:M_{\pi }\to X} whose fiber is the cone C F {\displaystyle CF} . To see this, notice the fiber over a...

3 to 0.5 mm. Each fiber bundle has a low density core region not occupied by fibers. The stress-strain response of the fiber bundles is nearly linear elastic...

engineering) Fiber bundle, a topological space that looks locally like a product space Optical fiber bundle, a cable consisting of a collection of fiber optics...

manifold) Connection (principal bundle) Connection (vector bundle) Connection (affine bundle) Connection (composite bundle) Connection (algebraic framework)...

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 and a continuous...

wrapped in bundles so they may be used to carry light into, or images out of confined spaces, as in the case of a fiberscope. Specially designed fibers are also...

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...

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...

{\displaystyle k(p)} is the residue field at p . {\displaystyle p.} Fibration Fiber bundle Fiber product Preimage theorem Zero set Lee, John M. (2011). Introduction...

In that example, the base space of a fiber bundle is pulled back, in the sense of precomposition, above. The fibers then travel along with the points in...

fiber space is a 3-manifold together with a decomposition as a disjoint union of circles. In other words, it is a S 1 {\displaystyle S^{1}} -bundle (circle...