Volume 11, issue 3 (2007)

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ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
$6j$–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 Uq(sl2) 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 S2 × S1. 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
Mathematical Subject Classification 2000
Primary: 57M27
Secondary: 57M50
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Publication
Received: 15 January 2007
Revised: 24 August 2007
Accepted: 25 July 2007
Published: 24 September 2007
Proposed: Walter Neumann
Seconded: Joan Birman, Cameron Gordon
Authors
Francesco Costantino
7, Rue René Descartes IRMA
Strasbourg 67000
France