fiber bundle theory

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• Fiber bundle — In mathematics, in particular in topology, a fiber bundle (or fibre bundle) is a space which looks locally like a product space. It may have a different global topological structure in that the space as a whole may not be homeomorphic to a… …   Wikipedia

• Section (fiber bundle) — In the mathematical field of topology, a section (or cross section) of a fiber bundle, pi; : E rarr; B , over a topological space, B , is a continuous map, f : B rarr; E , such that pi; ( f ( x ))= x for all x in B .A section is a certain… …   Wikipedia

• Bundle — may refer to:In mathematics: * Fiber bundle, in particular in topology, a space that looks locally like a product space *Bundle (mathematics), a generalization of a fiber bundle dropping the condition of a local product structureIn medicine: *… …   Wikipedia

• Bundle gerbe — In mathematics, a bundle gerbe is a geometrical model of certain 1 gerbes with connection, or equivalently of a 2 class in Deligne cohomology. Topology U (1) principal bundles over a space M (see circle bundle) are geometrical realizations of 1… …   Wikipedia

• Fiber (mathematics) — In mathematics, the fiber of a point y under a function f : X → Y is the inverse image of { y } under f , that is, f^{ 1}({y})={x in X : f(x) = y}In a variant phrase, this is also called the fiber of f at y .In various applications, this is also… …   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

• Fiber-optic communication — An optical fiber junction box. The yellow cables are single mode fibers; the orange and blue cables are multi mode fibers: 50/125 µm OM2 and 50/125 µm OM3 fibers respectively. Fiber optic communication is a method of transmitting information from …   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

• Kaluza–Klein theory — In physics, Kaluza–Klein theory (or KK theory, for short) is a model that seeks to unify the two fundamental forces of gravitation and electromagnetism. The theory was first published in 1921 and was discovered by the mathematician Theodor Kaluza …   Wikipedia

• Principal bundle — In mathematics, a principal bundle is a mathematical object which formalizes some of the essential features of a Cartesian product X times; G of a space X with a group G . Analogous to the Cartesian product, a principal bundle P is equipped with… …   Wikipedia

• Einstein–Cartan theory — in theoretical physics extends general relativity to correctly handle spin angular momentum. As the master theory of classical physics general relativity has one known flaw: it cannot describe spin orbit coupling , i.e., exchange of intrinsic… …   Wikipedia