Title: Equivariant Maps Which are Self Homotopy Equivalences
Abstract: The aim of this note is (i) to give (in §2) a precise statement and proof of the (to some extent well-known) fact that the most elementary homotopy theory of âsimplicial sets on which a fixed simplicial group H actsâ is equivalent to the homotopy theory of âsimplicial sets over the classifying complex $\bar WH$", and (ii) to use this (in §1) to prove a classification theorem for simplicial sets with an H-action, which provides classifying complexes for their equivariant maps which are self homotopy equivalences.