## 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.

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