Calcul du cocycle JLO pour l'op\'erateur de Dirac classique

TL;DR

This paper discusses the classical result linking the short-time limit of the JLO cocycle of the Dirac operator to the de Rham current, relating to the local index theorem.

Contribution

It provides a concise account of a well-known result connecting the JLO cocycle and the local index theorem in the context of Dirac operators.

Findings

Identifies the short-time limit of the JLO cocycle with the de Rham current.

Connects the JLO cocycle to the -genus and fundamental class.

Clarifies the classical folklore result in index theory.

Abstract

We provide a short account of a classical folklore result in connection to the local index theorem, which identifies the short-time limit of the JLO cocycle of the Dirac operator to de Rham current obtained by the cap product of the fundamental class with the \^A-genus.