6j-symbols, hyperbolic structures and the Volume Conjecture

Abstract

We compute the asymptotical growth rate of a large family of $U_q(s{l}_2)$ $6j$-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.

17 pages, 3 figures. Published on Geometry & Topology 11 (2007)

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