Bohlen, Karsten and Schrohe, Elmar (2018) Getzler rescaling via adiabatic deformation and a renormalized index formula. JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES, 120. pp. 220-252. ISSN 0021-7824, 1776-3371
Full text not available from this repository. (Request a copy)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 integrating Lie groupoid. We then describe the heat kernel of a geometric Dirac operator via a functional calculus with values in the convolution algebra of sections of a rescaled bundle over the adiabatic groupoid. Finally, we calculate the right coefficient in the heat kernel expansion by deforming the Dirac operator into a polynomial coefficient operator over the resealed bundle and applying the Lichnerowicz theorem to the fibers of the groupoid and the Lie manifold. (C) 2017 Elsevier Masson SAS. All rights reserved.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | PSEUDODIFFERENTIAL-OPERATORS; DIRAC OPERATORS; MANIFOLDS; THEOREM; GROUPOIDS; CALCULUS; BOUNDARY; Lie manifold; Index theory; Groupoid |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 04 Oct 2019 10:28 |
| Last Modified: | 04 Oct 2019 10:28 |
| URI: | https://pred.uni-regensburg.de/id/eprint/13448 |
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