1-efficient triangulations and the index of a cusped hyperbolic 3-manifold
Geometric Topology
2016-01-20 v1
Abstract
In this paper we will promote the 3D index of an ideal triangulation T of an oriented cusped 3-manifold M (a collection of q-series with integer coefficients, introduced by Dimofte-Gaiotto-Gukov) to a topological invariant of oriented cusped hyperbolic 3-manifolds. To achieve our goal we show that (a) T admits an index structure if and only if T is 1-efficient and (b) if M is hyperbolic, it has a canonical set of 1-efficient ideal triangulations related by 2-3 and 0-2 moves which preserve the 3D index. We illustrate our results with several examples.
Keywords
Cite
@article{arxiv.1303.5278,
title = {1-efficient triangulations and the index of a cusped hyperbolic 3-manifold},
author = {Stavros Garoufalidis and Craig D. Hodgson and J. Hyam Rubinstein and Henry Segerman},
journal= {arXiv preprint arXiv:1303.5278},
year = {2016}
}
Comments
60 pages, 27 figures