Finiteness conditions in covers of Poincaré duality spaces

Jonathan A. Hillman

Abstract

A closed 4-manifold (or, more generally, a finite
PD_{4}-space) has a finitely dominated infinite
regular covering space if and only if either its universal
covering space is finitely dominated or it is finitely covered
by the mapping torus of a self homotopy equivalence of a
PD_{3}-complex.