Elliptic complexes on manifolds with boundary
- We show that elliptic complexes of (pseudo) differential operators on smooth compact manifolds with boundary can always be complemented to a Fredholm problem by boundary conditions involving global pseudodifferential projections on the boundary (similarly as the spectral boundary conditions of Atiyah, Patodi, and Singer for a single operator). We prove that boundary conditions without projections can be chosen if, and only if, the topological Atiyah-Bott obstruction vanishes. These results make use of a Fredholm theory for complexes of operators in algebras of generalized pseudodifferential operators of Toeplitz type which we also develop in the present paper.
| Author details: | Bert-Wolfgang SchulzeGND, Jörg SeilerORCiDGND |
|---|---|
| DOI: | https://doi.org/10.1007/s12220-018-0014-6 |
| ISSN: | 1050-6926 |
| ISSN: | 1559-002X |
| Title of parent work (English): | The journal of geometric analysis |
| Publisher: | Springer |
| Place of publishing: | New York |
| Publication type: | Article |
| Language: | English |
| Date of first publication: | 2018/03/19 |
| Publication year: | 2019 |
| Release date: | 2021/05/26 |
| Tag: | Atiyah-Bott obstruction; Elliptic complexes; Manifolds with boundary; Toeplitz-type pseudodifferential operators |
| Volume: | 29 |
| Issue: | 1 |
| Number of pages: | 51 |
| First page: | 656 |
| Last Page: | 706 |
| 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 / Green Open-Access |
