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.

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

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