A Lefschetz fixed point formula for elliptic quasicomplexes

In a recent paper with N. Tarkhanov, the Lefschetz number for endomorphisms (modulo trace class operators) of sequences of trace class curvature was introduced. We show that this is a well defined, canonical extension of the classical Lefschetz number and establish the homotopy invariance of this number. Moreover, we apply the results to show that the Lefschetz fixed point formula holds for geometric quasiendomorphisms of elliptic quasicomplexes.

Metadaten
Author details:	Daniel Wallenta
URN:	urn:nbn:de:kobv:517-opus-67016
Publication series (Volume number):	Preprints des Instituts für Mathematik der Universität Potsdam (2(2013)12)
Publication type:	Preprint
Language:	English
Publication year:	2013
Publishing institution:	Universität Potsdam
Release date:	2013/08/13
Tag:	Lefschetz number; Perturbed complexes; curvature; fixed point formula
Organizational units:	Mathematisch-Naturwissenschaftliche Fakultät / Institut für Mathematik
DDC 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
Collection(s):	Universität Potsdam / Schriftenreihen / Preprints des Instituts für Mathematik der Universität Potsdam, ISSN 2193-6943 / 2013
License (German):	Keine öffentliche Lizenz: Unter Urheberrechtsschutz