Contractible open 3-manifolds with free covering translation groups

Details Contractible open 3-manifolds with free covering translation groups Contractible open 3-manifolds with free covering translation groups

1996-12-06

arxiv.org/abs/math/9612214v1

Mathematics

Geometric Topology

Scientific paper

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.

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