Gerbes, Clifford modules and the index theorem

2003/02/10 by Michael K. Murray, Murray, Michael K., Michael A. Singer +2
Mathematics · #58J20 #Advanced Operator Algebra Research #Advanced Topics in Algebra #Differential Geometry (math.DG) #FOS: Mathematics #Holomorphic and Operator Theory #math.DG #msc:58J20

paper · pdf · doi:10.48550/arxiv.math/0302096

10 pages, LaTeX (Added eference to preprint math.DG/0302050 by T. Aristide)

openalex publication_date 2003/02/10 · arxiv created 2003/02/11 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Related

• On the relationship of gerbes to the odd families index theorem
• Index and small bundle gerbes
• Index character associated to the projective Dirac operator
• Transgression of the index gerbe
• Index theory on Pin manifolds