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 \(PD_3\)-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, \(PD_3\)-group, \(PD_4\)-complex.

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