Contractible open 3-manifolds which are not covering spaces

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...

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

Covering Spaces of 3-manifolds

We will say that a 3-manifold is almost compact if it can be obtained from a compact manifold N by removing a closed subset of dN. Then Theorem 1 is equivalent to the assertion that the universal covering of M is almost compact. A natural way to attempt to generalize Theorem 1 is to show that other coverings of M are almost compact. It was conjectured by Simon [Si] that if M is any compact P-ir...

Finite covering spaces of 3-manifolds

Following Perelman’s solution to the Geometrisation Conjecture, a ‘generic’ closed 3-manifold is known to admit a hyperbolic structure. However, our understanding of closed hyperbolic 3-manifolds is far from complete. In particular, the notorious Virtually Haken Conjecture remains unresolved. This proposes that every closed hyperbolic 3-manifold has a finite cover that contains a closed embedde...