The Jones polynomial and graphs on surfaces
| Venue: | J. Combin. Theory Ser. B |
| Citations: | 19 - 7 self |
BibTeX
@ARTICLE{Dasbach_thejones,
author = {Oliver T. Dasbach and David Futer and Efstratia Kalfagianni and Xiao-song Lin and Neal and W. Stoltzfus},
title = {The Jones polynomial and graphs on surfaces},
journal = {J. Combin. Theory Ser. B},
year = {}
}
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Abstract
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 Bollobás–Riordan–Tutte polynomial generalizes the Tutte polynomial of 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 Bollobás–Riordan–Tutte polynomial of a certain combinatorial map associated to a link projection. We give some applications of this approach. 1.
