The decomposition of 3-dimensional Poincaré complexes

Abstract

We show that if the fundamental group of an orientable PD3-complex has infinitely many ends then it is either a proper free product or virtually free of finite rank. It follows that every PD3-complex is finitely covered by one which is homotopy equivalent to a connected sum of aspherical PD3-complexes and copies of $S^1\times S^2$ . Furthermore, it is shown that any torsion element of the fundamental group of an orientable PD3-complex has finite centraliser.