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 |
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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 |