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The geometry and physics of knots. (English) Zbl 0696.57002
Geometry and Physics, Proc. Miniconf., Canberra/Aust. 1989, Proc. Cent. Math. Anal. Aust. Natl. Univ. 22, 1-17 (1989).
[For the entire collection see Zbl 0678.00018.]
Brief but very informative survey of recent results devoted to a new approach to the Jones polynomial invariants of knots based on modern ideas of Topological Field Theory developed by E. Witten. The main idea of Witten is to connect Jones polynomial invariants with some expectation values of observables in special topological quantum field theory in three dimensions. The author considers related questions connected with this theme, for example: Donaldson invariants, relation between 2- dimensional field theory and topological field theory, quantization problem and connection with holomorphic vector bundles on Riemann surfaces etc.
Reviewer: M.Monastyrsky

MSC:
57M25 Knots and links in the \(3\)-sphere (MSC2010)
57-02 Research exposition (monographs, survey articles) pertaining to manifolds and cell complexes