Contractible $3$-manifolds of finite genus at infinity

Connectedness at Infinity of Complete Kähler Manifolds

One of the main purposes of this paper is to prove that on a complete Kähler manifold of dimension m, if the holomorphic bisectional curvature is bounded from below by -1 and the minimum spectrum λ1(M) ≥ m2, then it must either be connected at infinity or isometric to R×N with a specialized metric, with N being compact. Generalizations to complete Kähler manifolds satisfying a weighted Poincaré...

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...

Collisions at infinity in hyperbolic manifolds

For a complete, finite volume real hyperbolic n-manifold M , we investigate the map between homology of the cusps of M and the homology of M . Our main result provides a proof of a result required in a recent paper of Frigerio, Lafont, and Sisto.

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