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Morse theory indomitable. (English) Zbl 0685.58009

This paper is a beautiful survey of the last fifty year’s progress in Morse theory with milestones Thom, Smale, Witten and Floer. Starting with his own half-space approach which led him to the celebrated periodicity theorems, the author describes the birth of the Thom-Smale-Witten complex of descending cells of the function f: \(M\to {\mathbb{R}}\), which yields the cohomology of the manifold M. Witten’s harmonic oscillator approach is expressed, and an outlook to the infinite-dimensional case is given by reviewing the works made by Atiyah, the author, and Floer. There is a lot of stories added with people like Steenrod, Morse, Thom, Smale, Wilson, Witten, Atiyah, Sternberg, Guillemin or Mumford, interlard with the author’s indomitable humour.
Reviewer: V.Zoller

MSC:

58E05 Abstract critical point theory (Morse theory, Lyusternik-Shnirel’man theory, etc.) in infinite-dimensional spaces
58-02 Research exposition (monographs, survey articles) pertaining to global analysis
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References:

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