Volume 5, issue 1 (2005)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 24
Issue 6, 2971–3570
Issue 5, 2389–2970
Issue 4, 1809–2387
Issue 3, 1225–1808
Issue 2, 595–1223
Issue 1, 1–594

Volume 23, 9 issues

Volume 22, 8 issues

Volume 21, 7 issues

Volume 20, 7 issues

Volume 19, 7 issues

Volume 18, 7 issues

Volume 17, 6 issues

Volume 16, 6 issues

Volume 15, 6 issues

Volume 14, 6 issues

Volume 13, 6 issues

Volume 12, 4 issues

Volume 11, 5 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 4 issues

Volume 7, 4 issues

Volume 6, 5 issues

Volume 5, 4 issues

Volume 4, 2 issues

Volume 3, 2 issues

Volume 2, 2 issues

Volume 1, 2 issues

The Journal
About the Journal
Editorial Board
Subscriptions
 
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
 
ISSN 1472-2739 (online)
ISSN 1472-2747 (print)
Author Index
To Appear
 
Other MSP Journals
On the Mahler measure of Jones polynomials under twisting

Abhijit Champanerkar and Ilya Kofman

Algebraic & Geometric Topology 5 (2005) 1–22

arXiv: math.GT/0404236

Abstract

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.

Keywords
Jones polynomial, Mahler measure, Temperley–Lieb algebra, hyperbolic volume
Mathematical Subject Classification 2000
Primary: 57M25
Secondary: 26C10
References
Forward citations
Publication
Received: 13 October 2004
Revised: 6 November 2004
Accepted: 7 December 2004
Published: 5 January 2005
Authors
Abhijit Champanerkar
Department of Mathematics
Barnard College
Columbia University
3009 Broadway
New York NY 10027
USA
Ilya Kofman
Department of Mathematics
Columbia University
2990 Broadway
New York NY 10027
USA