The Jones polynomial and graphs on surfaces

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• 作者：Oliver T. Dasbach ; David Futer ; Efstratia Kalfagianni ; Xiao-Song Lin ; Neal W. Stoltzfus
• 关键词：Knots ; Links ; Ribbon graphs ; Jones polynomial ; Kauffman bracket ; Tutte polynomial ; Bollobá ; s– ; Riordan– ; Tutte polynomial
• 刊名：Journal of Combinatorial Theory, Series B
• 出版年：2008
• 出版时间：March 2008
• 年：2008
• 卷：98
• 期：2
• 页码：384-399
• 全文大小：368 K

文摘

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 oriented ribbon graph associated to a link projection. We give some applications of this approach.