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Mathematics > Geometric Topology

arXiv:1412.0401 (math)
[Submitted on 1 Dec 2014 (v1), last revised 29 Apr 2015 (this version, v2)]

Title:Triangulations of 3-manifolds with essential edges

Authors:Craig D. Hodgson, J. Hyam Rubinstein, Henry Segerman, Stephan Tillmann
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Abstract:We define essential and strongly essential triangulations of 3-manifolds, and give four constructions using different tools (Heegaard splittings, hierarchies of Haken 3-manifolds, Epstein-Penner decompositions, and cut loci of Riemannian manifolds) to obtain triangulations with these properties under various hypotheses on the topology or geometry of the manifold. We also show that a semi-angle structure is a sufficient condition for a triangulation of a 3-manifold to be essential, and a strict angle structure is a sufficient condition for a triangulation to be strongly essential. Moreover, algorithms to test whether a triangulation of a 3-manifold is essential or strongly essential are given.
Comments: 30 pages, 14 figures. Exposition improved
Subjects: Geometric Topology (math.GT)
MSC classes: 57N10, 57Q15
Cite as: arXiv:1412.0401 [math.GT]
  (or arXiv:1412.0401v2 [math.GT] for this version)
  https://doi.org/10.48550/arXiv.1412.0401

Submission history

From: Henry Segerman [view email]
[v1] Mon, 1 Dec 2014 10:08:36 UTC (830 KB)
[v2] Wed, 29 Apr 2015 16:13:14 UTC (1,190 KB)
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