Open Access
Translator Disclaimer
2005 Experimental evidence for the Volume Conjecture for the simplest hyperbolic non-2–bridge knot
Stavros Garoufalidis, Yueheng Lan
Algebr. Geom. Topol. 5(1): 379-403 (2005). DOI: 10.2140/agt.2005.5.379

Abstract

Loosely speaking, the Volume Conjecture states that the limit of the nth colored Jones polynomial of a hyperbolic knot, evaluated at the primitive complex nth root of unity is a sequence of complex numbers that grows exponentially. Moreover, the exponential growth rate is proportional to the hyperbolic volume of the knot. We provide an efficient formula for the colored Jones function of the simplest hyperbolic non-2–bridge knot, and using this formula, we provide numerical evidence for the Hyperbolic Volume Conjecture for the simplest hyperbolic non-2–bridge knot.

Citation

Download Citation

Stavros Garoufalidis. Yueheng Lan. "Experimental evidence for the Volume Conjecture for the simplest hyperbolic non-2–bridge knot." Algebr. Geom. Topol. 5 (1) 379 - 403, 2005. https://doi.org/10.2140/agt.2005.5.379

Information

Received: 16 December 2004; Revised: 21 April 2005; Accepted: 6 May 2005; Published: 2005
First available in Project Euclid: 20 December 2017

zbMATH: 1092.57005
MathSciNet: MR2153123
Digital Object Identifier: 10.2140/agt.2005.5.379

Subjects:
Primary: 57N10
Secondary: 57M25

Keywords: $q$–difference equations , asymptotics , Character varieties , Fusion , Hyperbolic Volume Conjecture , Jones polynomial , Kauffman bracket , knots , m082 , recursion relations , skein module , SnapPea

Rights: Copyright © 2005 Mathematical Sciences Publishers

JOURNAL ARTICLE
25 PAGES


SHARE
Vol.5 • No. 1 • 2005
MSP
Back to Top