On some topological realizations of groups and homomorphisms

Abstract

Given a homomorphism of groups f : G → H, we construct a topological space Xf such that its group of homeomorphisms Aut(Xf) is isomorphic to G, its group of homotopy classes of self-homotopy equivalences E(Xf) is isomorphic to H and the natural map between Aut(Xf) and E(Xf) is f. In addition, we consider realization problems involving homology groups, homotopy groups and groups of automorphisms.