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The Lefschetz number of sequences of trace class curvature

  • For a sequence of Hilbert spaces and continuous linear operators the curvature is defined to be the composition of any two consecutive operators. This is modeled on the de Rham resolution of a connection on a module over an algebra. Of particular interest are those sequences for which the curvature is "small" at each step, e.g., belongs to a fixed operator ideal. In this context we elaborate the theory of Fredholm sequences and show how to introduce the Lefschetz number.

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Author:Nikolai Nikolaevich TarkhanovORCiDGND, Daniel Wallenta
Series (Serial Number):Preprints des Instituts für Mathematik der Universität Potsdam (1 (2012) 3)
Document Type:Preprint
Year of Completion:2012
Publishing Institution:Universität Potsdam
Release Date:2012/01/06
Tag:Lefschetz number; Perturbed complexes; curvature
Organizational units:Mathematisch-Naturwissenschaftliche Fakultät / Institut für Mathematik
Dewey Decimal Classification:5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik
MSC Classification:19-XX K-THEORY [See also 16E20, 18F25] / 19Kxx K-theory and operator algebras [See mainly 46L80, and also 46M20] / 19K56 Index theory [See also 58J20, 58J22]
55-XX ALGEBRAIC TOPOLOGY / 55Uxx Applied homological algebra and category theory [See also 18Gxx] / 55U05 Abstract complexes
58-XX GLOBAL ANALYSIS, ANALYSIS ON MANIFOLDS [See also 32Cxx, 32Fxx, 32Wxx, 46-XX, 47Hxx, 53Cxx](For geometric integration theory, see 49Q15) / 58Jxx Partial differential equations on manifolds; differential operators [See also 32Wxx, 35-XX, 53Cxx] / 58J10 Differential complexes [See also 35Nxx]; elliptic complexes
Collections:Universität Potsdam / Schriftenreihen / Preprints des Instituts für Mathematik der Universität Potsdam, ISSN 2193-6943 / 2012
Licence (German):License LogoKeine Nutzungslizenz vergeben - es gilt das deutsche Urheberrecht
Notes extern:RVK-Klassifikation: SI 990 , SK 300