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Index theorem and equivariant cohomology on the loop space

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Abstract

In this paper, extending ideas of Witten and Atiyah, we describe some relations of equivariant cohomology on the loop space of a manifold to the path integral representation of the index of the Dirac operator on a twisted spin complex. In particular, the natural extension of the Chern character to the whole loop space is described. Also it is shown that the non-zero free homotopy classes of the loop space have 0 measure for the index measures associated to the index problem.

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Authors and Affiliations

  1. Département de Mathématique, Université Paris-Sud, F-91405, Orsay, France

    Jean-Michel Bismut

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  1. Jean-Michel Bismut
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Communicated by A. Jaffe

This work was partially supported by the NSF grant MCS-8108814(A02) while the author was visiting the Institute for Advanced Study (Princeton)

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Bismut, JM. Index theorem and equivariant cohomology on the loop space. Commun.Math. Phys. 98, 213–237 (1985). https://doi.org/10.1007/BF01220509

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  • DOI: https://doi.org/10.1007/BF01220509

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