The Jones polynomial and graphs on surfaces
Geometric Topology
2008-02-14 v3 Combinatorics
Abstract
The Jones polynomial of an alternating link is a certain specialization of the Tutte polynomial of the (planar) checkerboard graph associated to an alternating projection of the link. The Bollobas-Riordan-Tutte polynomial generalizes the Tutte polynomial of planar graphs to graphs that are embedded in closed oriented surfaces of higher genus. In this paper we show that the Jones polynomial of any link can be obtained from the Bollobas-Riordan-Tutte polynomial of a certain oriented ribbon graph associated to a link projection. We give some applications of this approach.
Keywords
Cite
@article{arxiv.math/0605571,
title = {The Jones polynomial and graphs on surfaces},
author = {Oliver T. Dasbach and David Futer and Efstratia Kalfagianni and Xiao-Song Lin and Neal W. Stoltzfus},
journal= {arXiv preprint arXiv:math/0605571},
year = {2008}
}
Comments
19 pages, 9 figures, minor changes