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Remarks on Morse Theory

  • M. F. Atiyah
Part of the NATO Advanced Study Institutes Series book series (NSSB, volume 59)

Abstract

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.

Keywords

Function Space Gauge Transformation Absolute Minimum Closed Geodesic Morse Theory 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. [1]
    M. F. Atiyah and R. Bott, Yang-Mills and bundles over algebraic curves, Volume dedicated to V. K. Patodi to be published by the Indian Academy of Science.Google Scholar
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    M. F. Atiyah and J.D.S. Jones, Topological aspects of Yang-Mills theory, Comm. Math. Phys. 61 (1978), 97–118.MathSciNetADSMATHCrossRefGoogle Scholar
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    R. Bott, An application of the Morse theory to the topology of Lie groups, Bull. Soc. Math. France, 84 (1956), 251–281.MathSciNetMATHGoogle Scholar
  4. [4]
    G. B. Segal, The topology of spaces of rational functions. Acta Math. 143 (1979), 39–72.MathSciNetMATHCrossRefGoogle Scholar

Copyright information

© Plenum Press, New York 1980

Authors and Affiliations

  • M. F. Atiyah
    • 1
  1. 1.Mathematical InstituteUniversity of OxfordOxfordUK

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