Contractible open 3-manifolds with free covering translation groups

Contractible Open 3-manifolds with Free Covering Translation Groups

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 f...

End Reductions and Covering Translations of Contractible Open 3-manifolds

This paper uses Brin and Thickstun’s theory of end reductions of noncompact 3-manifolds to study groups of covering translations of irreducible contractible open 3-manifolds W which are not homeomorphic to R. We associate to W an object S(W ) called the simplicial complex of minimal R-irreducible end reductions of W . Whenever W covers another 3-manifold the group of covering translations is is...

On Covering Translations and Homeotopy Groups of Contractible Open N-manifolds

This paper gives a new proof of a result of Geoghegan and Mihalik which states that whenever a contractible open n-manifold W which is not homeomorphic to Rn is a covering space of an n-manifold M and either n ≥ 4 or n = 3 and W is irreducible, then the group of covering translations injects into the homeotopy group of W .

Contractible Open 3-manifolds Which Non-trivially Cover Only Non-compact 3-manifolds

Cartesian Products of Contractible Open Manifolds