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2005 On the Mahler measure of Jones polynomials under twisting
Abhijit Champanerkar, Ilya Kofman
Algebr. Geom. Topol. 5(1): 1-22 (2005). DOI: 10.2140/agt.2005.5.1


We show that the Mahler measures of the Jones polynomial and of the colored Jones polynomials converge under twisting for any link. Moreover, almost all of the roots of these polynomials approach the unit circle under twisting. In terms of Mahler measure convergence, the Jones polynomial behaves like hyperbolic volume under Dehn surgery. For pretzel links P(a1,,an), we show that the Mahler measure of the Jones polynomial converges if all ai, and approaches infinity for ai= constant if n, just as hyperbolic volume. We also show that after sufficiently many twists, the coefficient vector of the Jones polynomial and of any colored Jones polynomial decomposes into fixed blocks according to the number of strands twisted.


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Abhijit Champanerkar. Ilya Kofman. "On the Mahler measure of Jones polynomials under twisting." Algebr. Geom. Topol. 5 (1) 1 - 22, 2005.


Received: 13 October 2004; Revised: 6 November 2004; Accepted: 7 December 2004; Published: 2005
First available in Project Euclid: 20 December 2017

zbMATH: 1061.57007
MathSciNet: MR2135542
Digital Object Identifier: 10.2140/agt.2005.5.1

Primary: 57M25
Secondary: 26C10

Rights: Copyright © 2005 Mathematical Sciences Publishers


Vol.5 • No. 1 • 2005
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