• DOI:10.1112/jtopol/jts022
• Corpus ID: 119638522

Triangulations of hyperbolic 3‐manifolds admitting strict angle structures

@article{Hodgson2011TriangulationsOH,
  title={Triangulations of hyperbolic 3‐manifolds admitting strict angle structures},
  author={Craig Hodgson and J. Hyam Rubinstein and Henry Segerman},
  journal={Journal of Topology},
  year={2011},
  volume={5}
}

• C. Hodgson, J. Rubinstein, Henry Segerman
• Published 14 November 2011
• Mathematics
• Journal of Topology

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 that 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.