Dokument-ID Dokumenttyp Verfasser/Autoren Herausgeber Haupttitel Abstract Auflage Verlagsort Verlag Erscheinungsjahr Seitenzahl Schriftenreihe Titel Schriftenreihe Bandzahl ISBN Quelle der Hochschulschrift Konferenzname Quelle:Titel Quelle:Jahrgang Quelle:Heftnummer Quelle:Erste Seite Quelle:Letzte Seite URN DOI Abteilungen OPUS4-50810 Wissenschaftlicher Artikel Schulze, Bert-Wolfgang; Seiler, Jörg Elliptic complexes on manifolds with boundary We show that elliptic complexes of (pseudo) differential operators on smooth compact manifolds with boundary can always be complemented to a Fredholm problem by boundary conditions involving global pseudodifferential projections on the boundary (similarly as the spectral boundary conditions of Atiyah, Patodi, and Singer for a single operator). We prove that boundary conditions without projections can be chosen if, and only if, the topological Atiyah-Bott obstruction vanishes. These results make use of a Fredholm theory for complexes of operators in algebras of generalized pseudodifferential operators of Toeplitz type which we also develop in the present paper. New York Springer 2019 51 The journal of geometric analysis 29 1 656 706 10.1007/s12220-018-0014-6 Institut für Mathematik OPUS4-37974 Wissenschaftlicher Artikel Wallenta, Daniel A Lefschetz fixed point formula for elliptic quasicomplexes In a recent paper, 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. Basel Springer 2014 11 Integral equations and operator theor 78 4 577 587 10.1007/s00020-014-2122-4 Institut für Mathematik OPUS4-36489 Wissenschaftlicher Artikel Tarkhanov, Nikolai Nikolaevich The dirichlet to Neumann operator for elliptic complexes We define the Dirichlet to Neumann operator for an elliptic complex of first order differential operators on a compact Riemannian manifold with boundary. Under reasonable conditions the Betti numbers of the complex prove to be completely determined by the Dirichlet to Neumann operator on the boundary. Providence American Mathematical Soc. 2011 17 Transactions of the American Mathematical Society 363 12 6421 6437 Institut für Mathematik OPUS4-35735 Wissenschaftlicher Artikel Wallenta, D. 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. Basel Springer 2012 20 Integral equations and operator theor 73 4 517 536 10.1007/s00020-012-1983-7 Institut für Mathematik