Two-cocycle twists and Atiyah-Patodi-Singer index theory
- We construct eta- and rho-invariants for Dirac operators, on the universal covering of a closed manifold, that are invariant under the projective action associated to a 2-cocycle of the fundamental group. We prove an Atiyah-Patodi-Singer index theorem in this setting, as well as its higher generalisation. Applications concern the classification of positive scalar curvature metrics on closed spin manifolds. We also investigate the properties of these twisted invariants for the signature operator and the relation to the higher invariants.
| Author details: | Sara AzzaliORCiD, Charlotte Wahl |
|---|---|
| DOI: | https://doi.org/10.1017/S0305004118000427 |
| ISSN: | 0305-0041 |
| ISSN: | 1469-8064 |
| Title of parent work (English): | Mathematical Proceedings of the Cambridge Philosophical Society |
| Publisher: | Cambridge Univ. Press |
| Place of publishing: | New York |
| Publication type: | Article |
| Language: | English |
| Year of first publication: | 2019 |
| Publication year: | 2019 |
| Release date: | 2020/10/20 |
| Volume: | 167 |
| Issue: | 3 |
| Number of pages: | 51 |
| First page: | 437 |
| Last Page: | 487 |
| Organizational units: | Mathematisch-Naturwissenschaftliche Fakultät / Institut für Mathematik |
| DDC classification: | 5 Naturwissenschaften und Mathematik / 51 Mathematik |
| Peer review: | Referiert |
| Publishing method: | Open Access |
| Open Access / Green Open-Access |
