Aspherical 4-manifolds with elementary amenable fundamental group

James F. Davis and J.A.Hillman

Abstract

We shall complement and strengthen a result of Freedman and Quinn by showing that if the fundamental group of an aspherical compact 4-manifold with boundary is elementary amenable then it is either polycyclic or is a solvable Baumslag-Solitar group. Moreover, two such manifolds are homeomorphic if and only if their peripheral group systems are equivalent, and each such manifold is the boundary connected sum of an aspherical 4-manifold with prime boundary and a contractible 4-manifold.

Keywords: aspherical, boundary, elementary amenable, 4-manifold, polycyclic.

AMS Subject Classification: Primary 57M05; secondary 57P10.