A variant of Roe algebras for spaces with cylindrical ends with applications in relative higher index theory
- In this paper, we define a variant of Roe algebras for spaces with cylindrical ends and use this to study questions regarding existence and classification of metrics of positive scalar curvature on such manifolds which are collared on the cylindrical end. We discuss how our constructions are related to relative higher index theory as developed by Chang, Weinberger, and Yu and use this relationship to define higher rho-invariants for positive scalar curvature metrics on manifolds with boundary. This paves the way for the classification of these metrics. Finally, we use the machinery developed here to give a concise proof of a result of Schick and the author, which relates the relative higher index with indices defined in the presence of positive scalar curvature on the boundary.
| Author details: | Mehran SeyedhosseiniORCiDGND |
|---|---|
| DOI: | https://doi.org/10.4171/JNCG/457 |
| ISSN: | 1661-6952 |
| ISSN: | 1661-6960 |
| Title of parent work (English): | Journal of noncommutative geometry |
| Publisher: | European Mathematical Society |
| Place of publishing: | Zurich |
| Publication type: | Article |
| Language: | English |
| Date of first publication: | 2022/07/16 |
| Publication year: | 2022 |
| Release date: | 2024/08/09 |
| Tag: | Roe algebras; higher index theory; manifolds with boundary; manifolds with cylindrical ends; positive scalar curvature; rho-invariants |
| Volume: | 16 |
| Issue: | 2 |
| Number of pages: | 30 |
| First page: | 595 |
| Last Page: | 624 |
| Organizational units: | Mathematisch-Naturwissenschaftliche Fakultät / Institut für Mathematik |
| DDC classification: | 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik |
| Peer review: | Referiert |
| Publishing method: | Open Access / Gold Open-Access |
| DOAJ gelistet | |
| License (German): |  CC-BY - Namensnennung 4.0 International |
