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Knots, braids and statistical mechanics. (English) Zbl 0772.57008

Advances in differential geometry and topology, 149-184 (1990).
[For the entire collection see Zbl 0745.00022.]
This survey paper gives a readable exposition of the new polynomial invariants of knots, including the braid theory approach using the Hecke algebra, for the Homfly polynomial, and the analogous relation between the Kauffman polynomial and the Birman-Wenzl algebra.
The second part of the paper describes the use of vertex models arising from statistical mechanics and shows how these ideas can be used in constructing knot invariants.

MSC:

57M25 Knots and links in the \(3\)-sphere (MSC2010)
82B23 Exactly solvable models; Bethe ansatz

Citations:

Zbl 0745.00022