Spectral zeta-invariants lifted to coverings
- The canonical trace and the Wodzicki residue on classical pseudo-differential operators on a closed manifold are characterised by their locality and shown to be preserved under lifting to the universal covering as a result of their local feature. As a consequence, we lift a class of spectral zeta-invariants using lifted defect formulae which express discrepancies of zeta-regularised traces in terms of Wodzicki residues. We derive Atiyah's L-2-index theorem as an instance of the Z(2)-graded generalisation of the canonical lift of spectral zeta-invariants and we show that certain lifted spectral zeta-invariants for geometric operators are integrals of Pontryagin and Chern forms.
Author details: | Sara AzzaliORCiD, Sylvie PaychaORCiDGND |
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DOI: | https://doi.org/10.1090/tran/8067 |
ISSN: | 0002-9947 |
ISSN: | 1088-6850 |
Title of parent work (English): | Transactions of the American Mathematical Society |
Publisher: | American Mathematical Society |
Place of publishing: | Providence, RI |
Publication type: | Article |
Language: | English |
Date of first publication: | 2020/07/08 |
Publication year: | 2020 |
Release date: | 2023/04/13 |
Volume: | 373 |
Issue: | 9 |
Number of pages: | 42 |
First page: | 6185 |
Last Page: | 6226 |
Funding institution: | DFG German Research Foundation (DFG) European Commission |
Organizational units: | Mathematisch-Naturwissenschaftliche Fakultät / Institut für Mathematik |
DDC classification: | 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik |
Peer review: | Referiert |