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Getzler rescaling via adiabatic deformation and a renormalized index formula

Bohlen, Karsten ; Schrohe, Elmar



Abstract

We prove an index theorem of Atiyah-Singer type for Dirac operators on manifolds with a Lie structure at infinity (Lie manifolds for short). With the help of a renormalized supertrace, defined on a suitable class of regularizing operators, the proof of the index theorem relies on a resealing technique similar in spirit to Getzler's resealing. With a given Lie manifold we associate an appropriate ...

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