Elliptic quasicomplexes on compact closed manifolds
- We consider quasicomplexes of pseudodifferential operators on a smooth compact manifold without boundary. To each quasicomplex we associate a complex of symbols. The quasicomplex is elliptic if this symbol complex is exact away from the zero section. We prove that elliptic quasicomplexes are Fredholm. Moreover, we introduce the Euler characteristic for elliptic quasicomplexes and prove a generalisation of the Atiyah-Singer index theorem.
Author details: | D. Wallenta |
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DOI: | https://doi.org/10.1007/s00020-012-1983-7 |
ISSN: | 0378-620X |
Title of parent work (English): | Integral equations and operator theor |
Publisher: | Springer |
Place of publishing: | Basel |
Publication type: | Article |
Language: | English |
Year of first publication: | 2012 |
Publication year: | 2012 |
Release date: | 2017/03/26 |
Tag: | Elliptic complexes; Fredholm complexes; Index theory |
Volume: | 73 |
Issue: | 4 |
Number of pages: | 20 |
First page: | 517 |
Last Page: | 536 |
Organizational units: | Mathematisch-Naturwissenschaftliche Fakultät / Institut für Mathematik |
Peer review: | Referiert |