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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.

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Metadaten
Author details:D. Wallenta
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
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