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

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