End reductions and covering translations of contractible open 3-manifolds
by
Robert Myers
Oklahoma State University

We apply Brin and Thickstun's theory of end reductions of irreducible open 3-manifolds to the study of universal covering spaces W of irreducible 3-manifolds M with infinite fundamental groups. The main theorem implies that if W is not homeomorphic to Euclidean 3-space, then the group of covering translations acts without fixed points on the set of all isotopy classes of end reductions of W. This is used to give examples of W for which any M must have infinite cyclic fundamental group; moreover, unlike previous such examples these W contain no non-trivial planes.

Date received: January 31, 2001