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Gerbes, Clifford Modules and the Index Theorem

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Abstract

The use of bundle gerbes and bundle gerbe modules is considered as a replacement for the usual theory of Clifford modules on manifolds that fail to be spin. It is shown that both sides of the Atiyah-Singer index formula for coupled Dirac operators can be given natural interpretations using this language and that the resulting formula is still an identity.

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References

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Authors and Affiliations

  1. Department of Pure Mathematics, University of Adelaide, Adelaide, SA, 5005, Australia

    Michael K. Murray

  2. School of Mathematics, King's Buildings, University of Edinburgh, EH9 3JZ, Scotland, U.K.

    Michael A. Singer

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  1. Michael K. Murray
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  2. Michael A. Singer
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Murray, M.K., Singer, M.A. Gerbes, Clifford Modules and the Index Theorem. Annals of Global Analysis and Geometry 26, 355–367 (2004). https://doi.org/10.1023/B:AGAG.0000047514.71785.96

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  • DOI: https://doi.org/10.1023/B:AGAG.0000047514.71785.96

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