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On a certain value of the Kauffman polynomial

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Abstract

IfF L (a, x) is the Kauffman polynomial of a linkL we show thatF L (1, 2 cos 2π/5) is determind up to a sign by the rank of the homology of the 2-fold cover of the complement ofL. This value corresponds to a certain Wenzl subfactor defined by the Birman-Wenzl algebra, which we describe in simple terms. There also corresponds a “solvable” model in statistical mechanics similar to the 5-state Potts model. It is the 5-state case of a general model of Fateev and Zamolodchikov.

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Authors and Affiliations

  1. Department of Mathematics, University of California, 94720, Berkeley, CA, USA

    V. F. R. Jones

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  1. V. F. R. Jones
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Communicated by A. Jaffe

Research partially supported by National Science Foundation grant DMS 86-14345

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Jones, V.F.R. On a certain value of the Kauffman polynomial. Commun. Math. Phys. 125, 459–467 (1989). https://doi.org/10.1007/BF01218412

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  • DOI: https://doi.org/10.1007/BF01218412

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