6j–symbols, hyperbolic structures and the volume conjecture

Costantino, Francesco¹

¹ 7, Rue René Descartes IRMA, Strasbourg 67000, France

Geometry & topology, Tome 11 (2007) no. 3, pp. 1831-1854.

Résumé

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 $S^2\times S^1$. We answer this question for the infinite family of fundamental shadow links.
Corrections  The paper was republished with corrections on 19 October 2007.

Détail

DOI : 10.2140/gt.2007.11.1831

Keywords: Jones polynomial, volume conjecture, hyperbolic volume, $6j$–symbol, quantum invariant

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