On the equivariant 2-type of a G-space

Abstract

A classical theorem of Mac Lane and Whitehead states that the homotopy type of a topological space with trivial homotopy at dimensions 3 and greater can be reconstructed from its π1 and π2, and a cohomology class k3 /gE H3(π1, π2). More recently, Moerdijk and Svensson suggested the possibility of using Bredon cohomology to extend this result to the equivariant case, that is, for spaces X equipped with an action by a fixed group G. In this paper we carry out this suggestion and prove an analogue of the classical result in the equivariant case.