A computer search for contractible 3-manifolds

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...

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

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...

Cartesian Products of Contractible Open Manifolds

Computer Presentation of 3-Manifolds

Our goal is to describe an economic way of presenting 3-manifolds numerically. The idea consists in replacing 3-manifolds by cell complexes (their special spines) and encoding the spines by strings of integers. The encoding is natural, i.e., it allows one to operate with manifolds without decoding. We describe an application of the encoding to computer enumeration of 3-manifolds and give the re...