On Perrot’s Index Cocycles

Jonathan Block, Nigel Higson, Jesus Sanchez

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

We give a simplified version of a construction due to Denis Perrot that recovers the Todd class of the complexified tangent bundle of a smooth manifold from a JLO-type cyclic cocycle. The construction takes place within an algebraic framework, rather than the customary functional-analytic framework of the JLO theory. The series expansion for the exponential function is used in place of the heat kernel from the functional-analytic theory; the Dirac operator chosen is far from elliptic; and a remarkable new trace discovered by Perrot replaces the operator trace. In its full form, Perrot’s theory constitutes a wholly new approach to index theory. The account presented here covers most but not all of his approach.

Original languageEnglish (US)
Title of host publicationCyclic Cohomology at 40
Subtitle of host publicationAchievements and Future Prospects
EditorsAlain Connes, Alain Connes, Caterina Consani, Bjørn Ian Dundas, Masoud Khalkhali, Henri Moscovici
PublisherAmerican Mathematical Society
Pages29-62
Number of pages34
ISBN (Print)9781470469771
DOIs
StatePublished - 2023
EventVirtual Conference on Cyclic Cohomology at 40: Achievements and Future Prospects, 2021 - Virtual, Online
Duration: Sep 27 2021Oct 1 2021

Publication series

NameProceedings of Symposia in Pure Mathematics
Volume105
ISSN (Print)0082-0717
ISSN (Electronic)2324-707X

Conference

ConferenceVirtual Conference on Cyclic Cohomology at 40: Achievements and Future Prospects, 2021
CityVirtual, Online
Period9/27/2110/1/21

All Science Journal Classification (ASJC) codes

  • General Mathematics

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