Connes-Moscovici Residue Cocycle For Some Dirac-Type Operators

2021/05/21 by Ahmad Reza Haj Saeedi Sadegh, Sadegh, Ahmad Reza Haj Saeedi, Yiannis Loizides +3
Mathematics · Physics and Astronomy · #Advanced Operator Algebra Research #Differential Geometry (math.DG) #FOS: Mathematics #Functional Analysis (math.FA) #K-Theory and Homology (math.KT) #Noncommutative and Quantum Gravity Theories #Operator Algebras (math.OA) #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2105.10091

openalex publication_date 2021/05/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The residue cocycle associated to a suitable spectral triple is the key component of the Connes-Moscovici local index theorem in noncommutative geometry. We review the relationship between the residue cocycle and heat kernel asymptotics. We use a modified version of the Getzler calculus to compute the cocycle for a class of Dirac-type operators introduced by Bismut, obtained by deforming a Dirac operator by a closed 3-form B. We also compute the cocycle in low-dimensions when the 3-form B is not closed.

Citations

• On the heat equation and the index theorem
• Generalized Complex Geometry

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