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 |
|---|---|
| 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 |
