On a certain value of the Kauffman polynomial
type: Item
instance of: scholarly article
title: On a certain value of the Kauffman polynomial
zbMATH Open document ID: 0695.57003
DOI: 10.1007/BF01218412
published in: Communications in Mathematical Physics
publication date: 1989-01-01T00:00:00Z
review text: The author gives a formula for the Kauffman polynomial \(F_ K(a,x)\) for \(a=1\), \(x=2 \cos 2\pi /5\) in terms of a Seifert form for K, which shows that this value is determined (up to a sign) by the rank of the first homology mod 5 of the 2-fold branched cover of \(S^ 3\) (branched over the knot K). He describes the relation to a Wenzl subfactor coming from a quotient of the Birman-Wenzl algebra and explains the connections with a 5-state chiral Potts model in statistical mechanics.
Mathematics Subject Classification ID: 57M25
Mathematics Subject Classification ID: 46L99
Mathematics Subject Classification ID: 80A99
zbMATH DE Number: 4138782
zbMATH Keywords: Kauffman polynomial
zbMATH Keywords: Seifert form
zbMATH Keywords: Wenzl subfactor
zbMATH Keywords: Birman-Wenzl algebra
zbMATH Keywords: 5-state chiral Potts model in statistical mechanics
author: V. F. R. Jones
reviewed by: Wolfgang Heil
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf01218412
OpenAlex ID: W1971010497
description: scientific article; zbMATH DE number 4138782