Pseudo-Developing Maps for Ideal Triangulations I: Essential Edges and Generalised Hyperbolic Gluing Equations

Henry Segerman; Stephan Tillmann

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arXiv · 1107.1030

Pseudo-Developing Maps for Ideal Triangulations I: Essential Edges and Generalised Hyperbolic Gluing Equations

Henry Segerman·Stephan Tillmann

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Abstract

Let N be a topologically finite, orientable 3-manifold with ideal triangulation. We show that if there is a solution to the hyperbolic gluing equations, then all edges in the triangulation are essential. This result is extended to a generalisation of the hyperbolic gluing equations, which enables the construction of hyperbolic cone-manifold structures on N with singular locus contained in the 1-skeleton of the triangulation.

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BibTeX RIS

Henry Segerman, Stephan Tillmann. 2011-07-06. Pseudo-Developing Maps for Ideal Triangulations I: Essential Edges and Generalised Hyperbolic Gluing Equations. https://arxiv.org/abs/1107.1030

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