Homotopy types of 4-manifolds with 3-manifold fundamental groups

Abstract

We show that the homotopy type of a 4-manifold $M$ whose fundamental group is a finitely presentable $P{D}_3$-group $\pi$ and with $w_1(M)=w_1(\pi )$ is determined by $\pi$, ${\pi }_2(M)$, $k_1(M)$ and the equivariant intersection pairing ${\lambda }_M$.

arXiv commentv2: material on surgery deleted. New \S6