Connes-Moscovici Residue Cocycle For Some Dirac-Type Operators
Operator Algebras
2021-05-24 v1 Differential Geometry
Functional Analysis
K-Theory and Homology
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.
Keywords
Cite
@article{arxiv.2105.10091,
title = {Connes-Moscovici Residue Cocycle For Some Dirac-Type Operators},
author = {Ahmad Reza Haj Saeedi Sadegh and Yiannis Loizides and Jesus Sanchez},
journal= {arXiv preprint arXiv:2105.10091},
year = {2021}
}