Title of article :
The Jones polynomial and graphs on surfaces
Author/Authors :
Dasbach، نويسنده , , Oliver T. and Futer، نويسنده , , David and Kalfagianni، نويسنده , , Efstratia and Lin، نويسنده , , Xiao-Song and Stoltzfus، نويسنده , , Neal W.، نويسنده ,
Issue Information :
روزنامه با شماره پیاپی سال 2008
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.
s 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.
Keywords :
knots , Ribbon graphs , Kauffman bracket , Tutte polynomial , Bollob?s–Riordan–Tutte polynomial , links , Jones polynomial
Journal title :
Journal of Combinatorial Theory Series B
Journal title :
Journal of Combinatorial Theory Series B