Large time limit and local L-2-index theorems for families
- We compute explicitly, and without any extra regularity assumptions, the large time limit of the fibrewise heat operator for Bismut-Lott type superconnections in the L-2-setting. This is motivated by index theory on certain non-compact spaces (families of manifolds with cocompact group action) where the convergence of the heat operator at large time implies refined L-2-index formulas. As applications, we prove a local L-2-index theorem for families of signature operators and an L-2-Bismut-Lott theorem, expressing the Becker-Gottlieb transfer of flat bundles in terms of Kamber-Tondeur classes. With slightly stronger regularity we obtain the respective refined versions: we construct L-2-eta forms and L-2-torsion forms as transgression forms.
Author details: | Sara AzzaliORCiD, Sebastian Goette, Thomas Schick |
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DOI: | https://doi.org/10.4171/JNCG/203 |
ISSN: | 1661-6952 |
ISSN: | 1661-6960 |
Title of parent work (English): | Journal of noncommutative geometry |
Publisher: | EMS Publ. |
Place of publishing: | Zürich |
Publication type: | Article |
Language: | English |
Year of first publication: | 2015 |
Publication year: | 2015 |
Release date: | 2017/03/27 |
Tag: | L-2-invariants; Local index theory; eta forms; torsion forms |
Volume: | 9 |
Issue: | 2 |
Number of pages: | 44 |
First page: | 621 |
Last Page: | 664 |
Funding institution: | INdAM-Cofund fellowship; German Research Foundation (DFG) through the Institutional Strategy of the University of Gottingen; DFG special programme "Global Differential Geometry"; DFG-SFB TR "Geometric Partial Differential Equations"; Courant Research Center "Higher order structures in Mathematics" within the Gelman initiative of excellence |
Organizational units: | Mathematisch-Naturwissenschaftliche Fakultät / Institut für Mathematik |
Peer review: | Referiert |