Celebratio Mathematica — Rubinstein

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Works connected to Henry Segerman

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C. D. Hodgson, J. H. Rubinstein, H. Segerman, and S. Tillmann: “Veering triangulations admit strict angle structures,” Geom. Topol. 15 : 4 (2011), pp. 2073–2089. MR 2860987 Zbl 1246.57034 article

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Craig David Hodgson	Related
Stephan Tillmann	Related

C. D. Hodgson, J. H. Rubinstein, and H. Segerman: “Triangulations of hyperbolic 3-manifolds admitting strict angle structures,” J. Topol. 5 : 4 (2012), pp. 887–908. Zbl 06121970 ArXiv 1111.3168 article

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.

Henry Segerman	Related
Craig David Hodgson	Related