#### Volume 11, issue 3 (2007)

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

### Francesco Costantino

Geometry & Topology 11 (2007) 1831–1854
 arXiv: math.GT/0611399
##### Abstract

We compute the asymptotical growth rate of a large family of ${U}_{q}\left(s{l}_{2}\right)$ $6j$–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 ${S}^{2}×{S}^{1}$. We answer this question for the infinite family of fundamental shadow links.
Corrections  The paper was republished with corrections on 19 October 2007.

##### Keywords
Jones polynomial, volume conjecture, hyperbolic volume, $6j$–symbol, quantum invariant
Primary: 57M27
Secondary: 57M50