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Polynomials for links. (English) Zbl 0685.57001
This article gives an excellent organic survey of the new polynomial invariants in knot theory initiated by V. F. R. Jones. After giving a brief history of the knot theory before the appearance of the Jones polynomial, the author tersely describes the present impact of these invariants on knot theory. In the first four sections, unified expositions of combinatorial approaches to the new polynomial invariants are given, and applications to the Tait conjectures are explained. In Section 5, the approach through Hecke algebra and those related to quantum statistical mechanics are described, and the relation with the Yang-Baxter equations are explained. In the last section, some other important topics are mentioned, and some basic problems are presented.
Reviewer: M.Sakuma

57M25 Knots and links in the \(3\)-sphere (MSC2010)
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