English

Contractible open 3-manifolds with free covering translation groups

Geometric Topology 2016-09-07 v1

Abstract

This paper concerns the class of contractible open 3-manifolds which are ``locally finite strong end sums'' of eventually end-irreducible Whitehead manifolds. It is shown that whenever a 3-manifold in this class is a covering space of another 3-manifold the group of covering translations must be a free group. It follows that such a 3-manifold cannot cover a closed 3-manifold. For each countable free group a specific uncountable family of irreducible open 3-manifolds is constructed whose fundamental groups are isomorphic to the given group and whose universal covering spaces are in this class and are pairwise non-homeomorphic.

Keywords

Cite

@article{arxiv.math/9612214,
  title  = {Contractible open 3-manifolds with free covering translation groups},
  author = {Robert Myers},
  journal= {arXiv preprint arXiv:math/9612214},
  year   = {2016}
}