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