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On a certain value of the Kauffman polynomial. (English) Zbl 0695.57003

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.
Reviewer: W.Heil

MSC:

57M25 Knots and links in the \(3\)-sphere (MSC2010)
46L99 Selfadjoint operator algebras (\(C^*\)-algebras, von Neumann (\(W^*\)-) algebras, etc.)
80A99 Thermodynamics and heat transfer
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