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arXiv · 2207.13411

On Perrot's index cocycles

Jonathan Block·Nigel Higson·Jesus Sanchez Jr
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Abstract

We shall present a simplified version of a construction due to Denis Perrot that recovers the Todd class of the complexified tangent bundle from a JLO-type cyclic cocycle. The construction takes place within an algebraic framework, rather than the customary functional-analytic framework for 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 this approach.

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Jonathan Block, Nigel Higson, Jesus Sanchez Jr. 2022-07-27. On Perrot's index cocycles. https://arxiv.org/abs/2207.13411

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