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Gerbes, Clifford modules and the index theorem

Michael K. Murray·Michael A. Singer
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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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Michael K. Murray, Michael A. Singer. 2003-02-11. Gerbes, Clifford modules and the index theorem. https://arxiv.org/abs/math/0302096

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