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Knots, braids, statistical mechanics and von Neumann algebras. (English) Zbl 0758.57002

The paper presents 2 lectures, the first one on polynomial invariants of knots and links and their relations to statistical mechanics and quantum field theory, the second one on the origin of the new invariants via braids and von Neumann algebras, finishing with Witten’s approach and the recent Vassiliev invariants of knots. It is written in the style of a report, without any proofs, and contains a large amount of information in a condensed way, so it can serve as a general orientation and guide in this exploding field of mathematics initiated by the author.

MSC:

57-02 Research exposition (monographs, survey articles) pertaining to manifolds and cell complexes
81-02 Research exposition (monographs, survey articles) pertaining to quantum theory
57M25 Knots and links in the \(3\)-sphere (MSC2010)
46L37 Subfactors and their classification