$PD_4$-complexes and 2-dimensional duality groups

Abstract

This paper is a synthesis and extension of three earlier papers on $PD_4$-complexes $X$ with fundamental group $\pi$ such that $c.d.\pi=2$ and $\pi$ has one end. Our goal is to show that the homotopy types of such complexes are determined by $\pi$, the Stiefel-Whitney classes and the equivariant intersection pairing on $\pi_2(X)$. We achieve this under further conditions on $\pi$.