On Poincaré duality for pairs (G,W)

Abstract

Let G be a group and W a G-set. In this work we prove a result that describes geometrically, for a Poincaré duality pair .G; W /, the set of representatives for the G-orbits in W and the family of isotropy subgroups. We also prove, through a cohomological invariant, a necessary condition for a pair .G; W / to be a Poincaré duality pair when W is infinite.