@inproceedings{6802f91c0c204052b58227d4b635a392,
title = "On Perrot{\textquoteright}s Index Cocycles",
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{\textquoteright}s theory constitutes a wholly new approach to index theory. The account presented here covers most but not all of his approach.",
author = "Jonathan Block and Nigel Higson and Jesus Sanchez",
note = "Funding Information: 2020 Mathematics Subject Classification. Primary 19D55, 19K56; Secondary 58J40. Key words and phrases. Index theory, cyclic cohomology, pseudodifferential operators. The second and third authors were partially supported by NSF grant DMS-1952669. Publisher Copyright: {\textcopyright} 2023 American Mathematical Society.; Virtual Conference on Cyclic Cohomology at 40: Achievements and Future Prospects, 2021 ; Conference date: 27-09-2021 Through 01-10-2021",
year = "2023",
doi = "10.1090/pspum/105/02",
language = "English (US)",
isbn = "9781470469771",
series = "Proceedings of Symposia in Pure Mathematics",
publisher = "American Mathematical Society",
pages = "29--62",
editor = "Alain Connes and Alain Connes and Caterina Consani and Dundas, {Bj{\o}rn Ian} and Masoud Khalkhali and Henri Moscovici",
booktitle = "Cyclic Cohomology at 40",
address = "United States",
}