Morse theory indomitable
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.
scientific article; zbMATH DE number 4122875