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Mahler measure of the Jones polynomial, part II
by
Ilya Kofman
Columbia University
Coauthors: Abhijit Champanerkar
The Mahler measure of the Alexander polynomial (Silver, Williams) and A-polynomial (Boyd, Rodriguez-Villegas) has been related to the volume of the knot complement. We show that the Mahler measure of the Jones polynomial converges under twisting in any link diagram. In this respect, the Jones polynomial, like the Alexander polynomial, behaves like hyperbolic volume under Dehn surgery. For torus knots, we obtain the explicit limit from the HOMFLY polynomial. The proof combines the representation theory of braid groups with linear skein theory. For twisting on two or three strands, we use the spanning tree expansion of the Jones polynomial to provide explicit formulas which extend previously known results.
Date received: December 10, 2003
Copyright © 2003 by the author(s). The author(s) of this work and the organizers of the conference have granted their consent to include this abstract in Topology Atlas. Document # camw-12.