Determining hyperbolicity of compact orientable 3-manifolds with torus boundary
Geometric Topology
2019-02-01 v5
Abstract
Thurston's hyperbolization theorem for Haken manifolds and normal surface theory yield an algorithm to determine whether or not a compact orientable 3-manifold with nonempty boundary consisting of tori admits a complete finite-volume hyperbolic metric on its interior. A conjecture of Gabai, Meyerhoff, and Milley reduces to a computation using this algorithm.
Keywords
Cite
@article{arxiv.1410.7115,
title = {Determining hyperbolicity of compact orientable 3-manifolds with torus boundary},
author = {Robert C. Haraway},
journal= {arXiv preprint arXiv:1410.7115},
year = {2019}
}
Comments
13 pages; supported in part by NSF grant DMS-1006553. Edit: 21/03/2015: clarification about solid torus glued to itself along two annuli. Edit: 30/07/2015: fixed error in sketch of Theorem 3's proof. Edit: 15/11/2016: improved T2xI test. Edit: 31/01/2019: significant rewrite in preparation for submission to journal