1-efficient triangulations and the index of a cusped hyperbolic 3-manifold

By Stavros Garoufalidis, Craig Hodgson, J. Hyam Rubinstein, Henry Segerman. 2013

55 citations recorded by the source corpus.

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 and 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. 57N10, 57M50; 57M25

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/f71352b8adec36762731299a634b295a6cb8be6c

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Geometry and Topology

1. Matthias Goerner
2. Stavros Garoufalidis
3. C. Zickert
4. Tudor Dimofte
5. Sergei Gukov
6. P. Sułkowski

In Mathematical Physics

1. Matthias Goerner
2. Stavros Garoufalidis
3. C. Zickert
4. Tudor Dimofte

Citations in the corpus

• Gluing equations for PGL(n, ℂ)–representations of 3–manifolds (2012, background): “(b) The loop invariants of [7] (c) The 3D index of [6, 5, 10, 11] The input of [4] is an ideal triangulation T of a 3-manifold with torus boundary components, and the output is a polynomial in q-commuting variables (one per meridian and longitude of each torus boundary component).”