English

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.

Keywords

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

R2 v1 2026-06-21T18:32:41.692Z