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The Jones polynomial and dessins d'enfant | | Oliver T. Dasbach
; David Futer
; Efstratia Kalfagianni
; Xiao-Song Lin
; Neal W. Stoltzfus
; | | Date: |
21 May 2006 | | Subject: | Geometric Topology; 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 plolynomial of planar graphs to graphs that are embedded in closed surfaces of higher genus (i.e. dessins d’enfant).
In this paper we show that the Jones polynomial of any link can be obtained from the Bollobas-Riordan-Tutte polynomial of a certain dessin associated to a link projection. We give some applications of this approach. | | Source: | arXiv, math/0605571 | | Services: | Forum | Review | PDF | Favorites | |
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