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.

Download full text files

Export metadata

Additional Services

Share in Twitter Search Google Scholar Statistics
Author:Nikolai Tarkhanov, 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