Unsigned state models for the Jones polynomial

Details Unsigned state models for the Jones polynomial Unsigned state models for the Jones polynomial

2007-10-22

arxiv.org/abs/0710.4152v2

Ann. Comb., 15 (2011) 127-146

Mathematics

Geometric Topology

Minor corrections. To appear in Annals of Combinatorics

Scientific paper

10.1007/s00026-011-0087-4

It is well a known and fundamental result that the Jones polynomial can be expressed as Potts and vertex partition functions of signed plane graphs. Here we consider constructions of the Jones polynomial as state models of unsigned graphs and show that the Jones polynomial of any link can be expressed as a vertex model of an unsigned embedded graph. In the process of deriving this result, we show that for every diagram of a link in the 3-sphere there exists a diagram of an alternating link in a thickened surface (and an alternating virtual link) with the same Kauffman bracket. We also recover two recent results in the literature relating the Jones and Bollobas-Riordan polynomials and show they arise from two different interpretations of the same embedded graph.

Affiliated with

Also associated with

No associations

Rating

Unsigned state models for the Jones polynomial does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Unsigned state models for the Jones polynomial, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Unsigned state models for the Jones polynomial will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-455590