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

Jonathan A. Hillman

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 ${\lambda }_M$.

Keywords: 4-manifold, homotopy type, $P{D}_3$-group, $P{D}_4$-complex.

AMS Subject Classification: Primary 57M13; secondary 57P10.