Jones, V. F. R. Commuting transfer matrices and link polynomials. (English) Zbl 0774.57005 Int. J. Math. 3, No. 2, 205-212 (1992). Guided by ideas from statistical mechanics, more specifically the use of the Yang-Baxter equation with a spectral parameter to obtain exactly solvable models, the author describes a procedure to produce examples of non-equivalent links with identical Jones and HOMFLY polynonials. The procedure includes mutation as a special case but goes well beyond it. The Kauffman polynomial is in general not preserved. The results provide examples with small crossing numbes, e.g. the pair \(4_ 1\#4_ 1\) and \(8_ 1\) or the pair \(8_ 8\) and \(10_{129}\) each have the same Jones polynomial. Reviewer: E.Vogt (Berlin) Cited in 1 ReviewCited in 4 Documents MSC: 57M25 Knots and links in the \(3\)-sphere (MSC2010) 82B23 Exactly solvable models; Bethe ansatz Keywords:Yang-Baxter equation with a spectral parameter; exactly solvable models; non-equivalent links with identical Jones and HOMFLY polynonials × Cite Format Result Cite Review PDF Full Text: DOI