6j-symbols, hyperbolic structures and the Volume Conjecture

Details 6j-symbols, hyperbolic structures and the Volume Conjecture 6j-symbols, hyperbolic structures and the Volume Conjecture

2006-11-13

arxiv.org/abs/math/0611399v4

Geometry & Topology 11 (2007), 1831-1853

Mathematics

Geometric Topology

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

Scientific paper

We compute the asymptotical growth rate of a large family of $U_q(sl_2)$ $6j$-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.

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