The Jones polynomial and graphs on surfaces

被引：90

作者：

Dasbach, Oliver T. ^{[1
]}

Futer, David ^{[2
]}

Kalfagianni, Efstratia ^{[2
]}

Lin, Xiao-Song

Stoltzfus, Neal W. ^{[1
]}

机构：

[1] Louisiana State Univ, Dept Math, Baton Rouge, LA 70803 USA

[2] Michigan State Univ, Dept Math, E Lansing, MI 48824 USA

来源：

JOURNAL OF COMBINATORIAL THEORY SERIES B | 2008年 / 98卷 / 02期

基金：

美国国家科学基金会;

关键词：

knots; links; ribbon graphs; Jones polynomial; Kauffman bracket; Tutte polynomial; Bollobas-Riordan-Tutte polynomial;

D O I：

10.1016/j.jctb.2007.08.003

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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 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. (C) 2007 Published by Elsevier Inc.

引用

页码：384 / 399

页数：16

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