fibergrupper
Fiber groups, in mathematics, refer to the structure group of a fiber bundle. A fiber bundle consists of a total space E, a base space B, a typical fiber F, and a projection π: E → B, together with local trivializations that identify π^{-1}(U) with U × F for open sets U ⊂ B. The structure group G is a topological (often Lie) group that acts on F by homeomorphisms or linear maps, and the bundle is glued together by transition functions g_ij: U_i ∩ U_j → G.
A principal G-bundle is a fundamental example: the fiber is G itself and G acts on itself
Common structure groups include GL(n, R), GL(n, C), SO(n), and U(n). The tangent bundle of a smooth
Classification and applications: For suitable base spaces X, isomorphism classes of principal G-bundles correspond to homotopy