On a certain value of the Kauffman polynomial
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.
5-state chiral Potts model in statistical mechanics
scientific article; zbMATH DE number 4138782