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On the Fixed Point Formula and the Rigidity Theorems of Witten Lectures at Cargése 1987

  • Raoul Bott
Part of the NATO ASI Series book series (NSSB, volume 185)

Abstract

These lectures are meant as an introduction to the interesting ideas which had their origin on the one hand in some string theoretic considerations of Witten and on the other in the more topological considerations of Landweber, Stong, Ochanine, and others [12]. These two diverse points of view have spawned a subject called “Elliptic cohomology” and so, in a sense, these are introductory lectures to that subject also. However my point of view will be rather different. My aim is - grosso modo - to show how this whole development fits into the framework of an old fixed point theorem which Atiyah and I proved some 25 years ago, and for which I would in any case like to make some propaganda amongst my physicist friends.

Keywords

Meromorphic Function Modular Form Dirac Operator Fixed Point Theorem Loop Space 
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

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    Atiyah, M.F. and Bott, R., A Lefschetz fixed point formula for elliptic complexes I, Ann. of Math. 86, 1967.Google Scholar
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    Atiyah, M.F. and Bott, R., A Lefschetz fixed point formula for elliptic complexes II, Ann. of Math. 88, 1968.Google Scholar
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    Atiyah, M.F. and Bott, R., The Moment Map and equivariant cohomology, Topology, Vol. 23 # 1, 1984, 1–28.MathSciNetzbMATHCrossRefGoogle Scholar
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    Atiyah, M.F. and Hirzebruch, F., Spin manifolds and group actions, “Memoires dedicated to Georges DeRham”, Springer-Verlag, New York-Heidelberg-Berlin, 1970, 18–28.Google Scholar
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    Landweber, P.S., and Stong, R.E., Circle actions on Spin Manifolds and Characteristic numbers, Rutgers Preprint 1985, to appear in Topology.Google Scholar
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    Ochanine, S., Genres elliptiques equivariants, Université de Paris Sud Preprint 1986.Google Scholar
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    Taubes, C., S 1actions and elliptic genera, Harvard Preprint 1987.Google Scholar
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    Witten, E., Global Anomalies in String Theory in “Anomalies, Geometry and Topology”, ed. by W. Bardeen and A. White, World Scientific, 1985.Google Scholar
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    Witten, E., The index of the Dirac operator in Loop Space, Princeton Preprint PUPT-1050, to be published in the Proc. of the Conf. on Elliptic Curves and Modular Forms in Alg. Topology (IAS, September, 1986).Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1988

Authors and Affiliations

  • Raoul Bott
    • 1
  1. 1.Department of MathematicsHarvard UniversityCambridgeUSA

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