Contractible open 3-manifolds with free covering translation groups

✍ Scribed by Robert Myers

• Publisher: Elsevier Science
• Year: 1999
• Tongue: English
• Weight: 129 KB
• Volume: 96
• Category: Article
• ISSN: 0166-8641
• DOI: 10.1016/s0166-8641(98)00047-9

✦ Synopsis

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.