On the spaces of self homotopy equivalences for fibre spaces

Abstract

If a base space B is simply connected, we had some results on G0(E) in the previous papers [16, 17, 18, 19]. Here we treat G0(£) for the case of a nonsimply connected base space B. Let G be an abelian group and let Aut(G) be its group of automorphisms. Denote by L(G, n+1) the classifying space for fibrations with fibre K(G, ri) and by W an Eilenberg-MacLane complex K(Aut(G), 1). Then we have the fibration :