## Geometry & Topology

### $6j$–symbols, hyperbolic structures and the volume conjecture

Francesco Costantino

#### Abstract

We compute the asymptotical growth rate of a large family of $Uq(sl2)$ $6j$–symbols and we interpret our results in geometric terms by relating them to volumes of hyperbolic truncated tetrahedra. We address a question which is strictly related with S Gukov’s generalized volume conjecture and deals with the case of hyperbolic links in connected sums of $S2×S1$. We answer this question for the infinite family of fundamental shadow links. Corrections  The paper was republished with corrections on 19 October 2007.

#### Article information

Source
Geom. Topol., Volume 11, Number 3 (2007), 1831-1854.

Dates
Revised: 24 August 2007
Accepted: 25 July 2007
First available in Project Euclid: 20 December 2017

https://projecteuclid.org/euclid.gt/1513799912

Digital Object Identifier
doi:10.2140/gt.2007.11.1831

Mathematical Reviews number (MathSciNet)
MR2350469

Zentralblatt MATH identifier
1132.57011

Subjects
Primary: 57M27: Invariants of knots and 3-manifolds
Secondary: 57M50: Geometric structures on low-dimensional manifolds

#### Citation

Costantino, Francesco. $6j$–symbols, hyperbolic structures and the volume conjecture. Geom. Topol. 11 (2007), no. 3, 1831--1854. doi:10.2140/gt.2007.11.1831. https://projecteuclid.org/euclid.gt/1513799912

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