Let G be a topological group and let P be a principal G-bundle over a based space B. We denote the gauge group of P by G(P) and the based gauge group of P by G0(P). Then the inclusion of the basepoint of B induces the exact sequence of topological groups 1 → G0(P) → G(P) → G → 1. We study the splitting of this exact sequence in the category of An-spaces and An-maps in connection with the triviality of the adjoint bundle of P and with the higher homotopy commutativity of G.
All Science Journal Classification (ASJC) codes
- General Mathematics
- Applied Mathematics