Projective criteria and constructions of acyclic \Gamma complexes
by
Tadeusz Kozniewski
Warsaw University

Let \Gamma be a group of finite virtual cohomological dimension. We give some criteria for the projectivity of modules over group rings R\Gamma. The projective criteria are then applied to obtain constructions of acyclic \Gamma complexes with various finiteness properties. In particular we show that if p is a prime then every proper, finite dimensional \Gamma complex X has a p-envelope, i.e. there exists a \Gamma complex Y which contains X so that Y is finite dimensional, Z/p acyclic and all isotropy groups in Y-X are finite p-groups. This is anologous to the existence result for p-envelopes proved by Jackowski, McClure and Oliver (Annals of Math. 135, 1992) in the case of actions of compact Lie groups.

Date received: April 15, 1998