Pseudo-Developing Maps for Ideal Triangulations I: Essential Edges and Generalised Hyperbolic Gluing Equations
Geometric Topology
2011-07-07 v1
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.
Cite
@article{arxiv.1107.1030,
title = {Pseudo-Developing Maps for Ideal Triangulations I: Essential Edges and Generalised Hyperbolic Gluing Equations},
author = {Henry Segerman and Stephan Tillmann},
journal= {arXiv preprint arXiv:1107.1030},
year = {2011}
}
Comments
19 pages, 8 figures, to appear in the proceedings of Jacofest