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Coincident link polynomials from commuting transfer matrices. (English) Zbl 0813.57004

Catto, Sultan (ed.) et al., Differential geometric methods in theoretical physics. Proceedings of the 20th international conference, June 3-7, 1991, New York City, NY, USA. Vol. 1-2. Singapore: World Scientific. 137-151 (1992).
Summary: Borrowing from an argument in statistical mechanics we give a machine for constructing pairs of links with the same skein polynomials. Examples are generally not mutants (Kauffman polynomials differ) and can have small crossing numbers, e.g. the coinicidence \(V_{4_ 1 \# 4_ 1} = V_{8_ 9}\) is explained.
For the entire collection see [Zbl 0801.00032].

MSC:

57M25 Knots and links in the \(3\)-sphere (MSC2010)
20F36 Braid groups; Artin groups