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...

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

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...

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...

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 )...

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...

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...

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")...

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...

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}...

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...

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...

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...

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...

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

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...

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,...

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...

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...

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...

tensor bundle a connection is needed, except for the special case of the exterior derivative of antisymmetric tensors. A tensor bundle is a fiber bundle where...

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...

functions from M to T. (More generally, we can have smooth sections of a fiber bundle T over M.) Examples of this M in physics include: In classical mechanics...

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...