Groups acting on finite dimensional spaces with finite stabilizers

Abstract

It is shown that every HF-group G of type FP admits a finite dimensional G-CWcomplex X with finite stabilizers and with the additional property that for each finite subgroup H, the fixed point subspace X H is contractible. This establishes conjecture (5.1.2) of The construction of X involves joining a family of spaces parametrized by the poset of non-trivial finite subgroups of G and ultimately relies on the theorem of Cornick and Kropholler that if M is a ZG-module which is projective as a ZH-module for all finite H G then M has finite projective dimension.