Triangulations of hyperbolic 3-manifolds admitting strict angle structures
Abstract
It is conjectured that every cusped hyperbolic 3-manifold has a decomposition into positive volume ideal hyperbolic tetrahedra (a "geometric" triangulation of the manifold). Under a mild homology assumption on the manifold we construct topological ideal triangulations which admit a strict angle structure, which is a necessary condition for the triangulation to be geometric. In particular, every knot or link complement in the 3-sphere has such a triangulation. We also give an example of a triangulation without a strict angle structure, where the obstruction is related to the homology hypothesis, and an example illustrating that the triangulations produced using our methods are not generally geometric.
Cite
@article{arxiv.1111.3168,
title = {Triangulations of hyperbolic 3-manifolds admitting strict angle structures},
author = {Craig D. Hodgson and J. Hyam Rubinstein and Henry Segerman},
journal= {arXiv preprint arXiv:1111.3168},
year = {2014}
}
Comments
28 pages, 9 figures. Minor edits and clarification based on referee's comments. Corrected proof of Lemma 7.4. To appear in the Journal of Topology