Pro-$p$ Poincaré-Duality groups of infinite rank

Abstract

We introduce the class of \textit{Generalized Poincaré-Duality groups}: i.e, pro-$p$ groups of infinite rank which satisfy a Poincaré-duality. We prove some basic properties of Generalized Poincaré-Duality groups, and show that under some conditions, a group that fits into an exact sequence of GPD groups must be a Demushkin group.