Bredon–Poincaré duality groups

Abstract

Abstract If G is a group which admits a manifold model for BG then G is a Poincaré duality group. We study a generalisation of Poincaré duality groups, introduced initially by Davis and Leary in [High-Dimensional Manifold Topology, World Scientific, Singapore (2003), 139–150], motivated by groups G with cocompact manifold models M for E̠G where MH is a contractible submanifold for all finite subgroups H of G. We give several sources of examples and constructions of these Bredon–Poincaré duality groups, including using the equivariant reflection group trick of Davis and Leary to construct examples of Bredon–Poincaré duality groups arising from actions on manifolds M where the dimensions of the submanifolds MH are specified. We classify Bredon–Poincaré duality groups in low dimensions, and discuss behaviour under group extensions and graphs of groups.