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Index theorems on manifolds with straight ends

Part of: Global differential geometry Partial differential equations on manifolds; differential operators

Published online by Cambridge University Press:  15 October 2012

Werner Ballmann ,
Jochen Brüning  and
Gilles Carron
Werner Ballmann
Affiliation:
Mathematisches Institut, Universität Bonn, Endenicher Allee 60, 53115 Bonn, Germany (email: hwbllmnn@math.uni-bonn.de) Max-Planck-Institut für Mathematik, Vivatsgasse 7, 53111 Bonn, Deutschland, Germany
Jochen Brüning
Affiliation:
Institut für Mathematik, Humboldt–Universität, Rudower Chaussee 5, 12489 Berlin, Germany (email: bruening@mathematik.hu-berlin.de)
Gilles Carron
Affiliation:
Département de Mathématiques, Université de Nantes, 2 rue de la Houssiniére, BP 92208, 44322 Nantes Cedex 03, France (email: Gilles.Carron@math.univ-nantes.fr)
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Abstract

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We study Fredholm properties and index formulas for Dirac operators over complete Riemannian manifolds with straight ends. An important class of examples of such manifolds are complete Riemannian manifolds with pinched negative sectional curvature and finite volume.

Keywords

Dirac operatorFredholm typenon-parabolicindex

MSC classification

Secondary: 53C20: Global Riemannian geometry, including pinching 58J20: Index theory and related fixed point theorems
Type
Research Article
Information
Compositio Mathematica , Volume 148 , Issue 6 , November 2012 , pp. 1897 - 1968
Copyright
Copyright © Foundation Compositio Mathematica 2012

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