6j–symbols, hyperbolic structures and the volume conjecture

Costantino, Francesco

doi:10.2140/gt.2007.11.1831

Download this article
	For screen
	For printing

Recent Issues

The Journal

Submission Guidelines

Submission Page

Policies for Authors

Ethics Statement

ISSN 1364-0380 (online)

ISSN 1465-3060 (print)

Author Index

To Appear

Other MSP Journals

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

Francesco Costantino

Geometry & Topology 11 (2007) 1831–1854

DOI: 10.2140/gt.2007.11.1831

arXiv: math.GT/0611399

Abstract

We compute the asymptotical growth rate of a large family of $U_{q} (s l_{2})$ $6 j$ –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.

Keywords

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

Mathematical Subject Classification 2000

Primary: 57M27

Secondary: 57M50

References

Forward citations

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

Volume 11, issue 3 (2007)