Morse theory indomitable
type: Item
instance of: scholarly article
title: Morse theory indomitable
zbMATH Open document ID: 0685.58009
DOI: 10.1007/BF02698544
published in: Publications Mathématiques
publication date: 1988-01-01T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/104046
review text: 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.
Mathematics Subject Classification ID: 58E05
Mathematics Subject Classification ID: 58-02
zbMATH DE Number: 4122875
zbMATH Keywords: moment map
zbMATH Keywords: symplectic geometry
zbMATH Keywords: survey
zbMATH Keywords: Thom-Smale-Witten complex
zbMATH Keywords: harmonic oscillator
MaRDI profile type: Publication
cites work: The Yang-Mills equations over Riemann surfaces
cites work: The moment map and equivariant cohomology
cites work: On the variation in the cohomology of the symplectic form of the reduced phase space
cites work: Morse theory for Lagrangian intersections
cites work: Puits multiples en mecanique semi-classique iv etude du complexe de witten
cites work: Differentiable dynamical systems
cites work: Q5791774
cites work: Supersymmetry and Morse theory
OpenAlex ID: W1995882555
author: Raoul Bott
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description: scientific article; zbMATH DE number 4122875