Contractible open 3-manifolds which non-trivially cover only non-compact 3-manifolds

Robert Myers

Contractible open 3-manifolds which non-trivially cover only non-compact 3-manifolds

Geometric Topology 2016-09-06 v1

Authors: Robert Myers

Abstract

Suppose $M$ is a closed, connected, orientable, \irr\ \3m\ such that $G=\pi_1(M)$ is infinite. One consequence of Thurston's geometrization conjecture is that the universal covering space $\widetilde{M}$ of $M$ must be \homeo\ to $\RRR$ . This has been verified directly under several different additional assumptions on $G$ . (See, for example, \cite{2}, \cite{3}, \cite{6}, \cite{19}.)

Keywords

contractible open 3-manifolds universal covering space geometrization conjecture irreducible 3-manifold non-compact 3-manifolds fundamental group

Cite

@article{arxiv.math/9606225,
  title  = {Contractible open 3-manifolds which non-trivially cover only non-compact 3-manifolds},
  author = {Robert Myers},
  journal= {arXiv preprint arXiv:math/9606225},
  year   = {2016}
}

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