Gerbes, Clifford modules and the index theorem

M K  Murray; M A  Singer

Gerbes, Clifford modules and the index theorem

M K Murray
, M A Singer

School of Mathematics

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	355-367
Number of pages	13
Journal	Annals of Global Analysis and Geometry
Volume	26
Issue number	4
Publication status	Published - Nov 2004

Keywords / Materials (for Non-textual outputs)

index theory
gerbes
twisted K-theory
Dirac operator
Clifford modules
ELLIPTIC OPERATORS
BUNDLE GERBES

Cite this

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title = "Gerbes, Clifford modules and the index theorem",

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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journal = "Annals of Global Analysis and Geometry",

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T1 - Gerbes, Clifford modules and the index theorem

AU - Murray, M K

AU - Singer, M A

PY - 2004/11

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N2 - 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.

AB - 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.

KW - index theory

KW - gerbes

KW - twisted K-theory

KW - Dirac operator

KW - Clifford modules

KW - ELLIPTIC OPERATORS

KW - BUNDLE GERBES

M3 - Article

SN - 0232-704X

VL - 26

SP - 355

EP - 367

JO - Annals of Global Analysis and Geometry

JF - Annals of Global Analysis and Geometry

IS - 4

ER -

Gerbes, Clifford modules and the index theorem

Abstract

Keywords / Materials (for Non-textual outputs)

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Cite this