Finitely dominated subnormal covers of 4-manifolds

Jonathan A. Hillman

Abstract

Let M be a closed 4-manifold which has a finitely dominated covering space associated to a subnormal subgroup G of infinite index in π=π₁(M). If G is FP₃, has finitely many ends and π is virtually torsion free then either M is aspherical or its universal covering space is homotopy equivalent to S² or S³. In the aspherical case such a subgroup is usually Z, a surface group or a PD₃-group. [This is a revision of a 1994 Sydney Research Report].

Keywords: finitely dominated, 4-manifold, Poincaré duality, subnormal.

AMS Subject Classification: Primary 57N13.