Regularised traces and Getzler’s rescaling revisited

Abstract: Inspired by Gilkey's invariance theory, Connes' deformation to the normal cone and Getzler's rescaling method, we single out a class of geometric operators among pseudodifferential operators acting on sections of a class of natural vector bundles, to which we attach a rescaling degree. This degree is then used to express regularised traces of geometric operators in terms of a rescaled limit of Wodzicki residues. When applied to complex powers of the square of a Dirac operator, this amounts to expressing the index of a Dirac operator in terms of a local residue involving the Getzler rescaled limit of its square.

This is joint work with Georges Habib.

geometric topologynumber theoryoperator algebrasrepresentation theory

Audience: researchers in the topic

( video )

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