Old and new link polynomials from the theory of exactly solvable models. (English) Zbl 0741.57008
Summary: A general theory is presented to construct link polynomials, topological invariants for knots and links, from exactly solvable (integrable) models. Representations of the braid group and the Markov traces on the representations are made through the general theory which is based on fundamental properties of the models. Various examples leading to Alexander, Jones, Kauffman and new link polynomials are explicitly shown. In a word, the soliton theory contains an essence of knot theory.
MSC:
| 57M25 | Knots and links in the \(3\)-sphere (MSC2010) |
Keywords:
exactly solvable models; Kauffman polynomial; link polynomials; topological invariants for knots and links; Representations of the braid group; Markov traces; Jones polynomial; Alexander polynomialReferences:
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