Heat kernels of perturbed operators and index theory on G-proper manifolds
| Autor: | Piazza, Paolo, Posthuma, Hessel, Song, Yanli, Tang, Xiang |
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| Rok vydání: | 2023 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | Let G be a connected, linear real reductive group and let X be a G-proper manifold without boundary. We give a detailed account of both the large and small time behaviour of the heat-kernel of perturbed Dirac operators, as a map from the positive real line to the Lafforgue algebra. As a first application, we prove that certain delocalized eta invariants associated to perturbed Dirac operators are well defined. We then prove index formulas relating these delocalized eta invariants to Atiyah-Patodi-Singer delocalized indices on G-proper manifolds with boundary. We apply these results to the definition of rho-numbers associated to G-homotopy equivalences between closed G-proper manifolds and to the study of their bordism properties. Comment: This article contains an updated and extended version of part of arXiv:210800982(v2). It is independent of arXiv:210800982(v3), and the two papers together supersede arXiv:210800982(v2). The discussion of perturbations of Dirac operators in arXiv:210800982(v2) is corrected and included in this article |
| Databáze: | arXiv |
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