Determining hyperbolicity of compact orientable 3-manifolds with torus boundary

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.

arXiv comment13 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