Equivariant stable homotopy and Sullivan's conjecture

Abstract

Let G be a p-group, and let X be a G-complex. Let EG denote a contractible space on which G acts freely. By the "homotopy fixed point set" of X, we mean the fixed point set F(EG, X) G, where F(EG, X) denotes the function space of all maps EG ~ X, equipped with a G-action by 9f = 9f9-1. If we let * denote the one point space with trivial G-action, we may also consider the G-space F ( , ,X ) ; it is canonically G-homeomorphic to X. The G-map E G ~ , induces a map ~/: X G ~F( , , X) G. In [19], D. Sullivan proposed the following.