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The Walks Model of the Color Jones Polynomial and some Applications
by
Jesse S. F. Levitt
University of Southern California
Coauthors: Nicolle E. S. González, University of Southern California;
Mustafa Hajij, University of Southern Florida
The colored Jones polynomial is a quantum knot invariant that plays a central role in low dimensional topology. We review a walks along a braid model of the colored Jones polynomial that was refined by Armond from the work of Huynh and Lê. The walk model gives rise to ordered words in a q-Weyl algebra. We will discuss the computation of this invariant with applications to the Jones unknot conjecture as well as several limiting behaviors with applications to the calculation of the Mahler measure of a knot.
Date received: March 19, 2018
Copyright © 2018 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 # cboy-07.