Celebratio Mathematica — Atiyah

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M. F. Atiyah: “Remarks on Morse theory,” pp. 1–5 in Recent developments in gauge theories. Edited by G. ’t Hooft, C. Itzykson, A. Jaffe, H. Lehmann, P. K. Mitter, I. M. Singer, and R. Stora. NATO Advanced Study Institutes Series B. Physics. 59. Plenum Press (New York and London), 1980. Republished in Atiyah’s Collected works, vol. 5. incollection

Morse theory is a topological approach to the Calculus of Variations. It aims to relate the critical points of a functional to the topology of the function space on which the functional is defined. It is only directly applicable in special rather restrictive conditions, notably for problems involving one independent variable. However I will discuss a number of special examples, in some of which the Morse theory really works, and others in which it clearly fails but where nevertheless some aspects appear still to survive. These examples include those of physical interest and it would be interesting to investigate these further. One can make a number of speculations in this direction.

Pronob K. Mitter	Related
Arthur Jaffe	Related
Raymond Stora	Related
Gerardus ’t Hooft	Related
Isadore M. Singer	Related	Volume
Claude Itzykson	Related
Harry Paul Lehmann	Related