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Analysis of geometric operators on open manifolds: A groupoid approach

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Quantization of Singular Symplectic Quotients

Part of the book series: Progress in Mathematics ((PM,volume 198))

Abstract

The first five sections of this paper are a survey of algebras of pseudodifferential operators on groupoids. We thus review differentiable groupoids, the definition of pseudodifferential operators on groupoids, and some of their properties. We use then this background material to establish a few new results on these algebras, results that are useful for the analysis of geometric operators on non-compact manifolds and singular spaces. The first step is to establish that the geometric operators on groupoids are in our algebras. This then leads to criteria for the Fredholmness of geometric operators on suitable non-compact manifolds, as well as to an inductive procedure to study their essential spectra. As an application, we answer a question of Melrose on the essential spectrum of the Laplace operator on manifolds with multi-cylindrical ends.

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Author information

Authors and Affiliations

  1. Fachbereich 17-Mathematik, Universität Mainz, D-55099, Mainz, Germany

    Robert Lauter

  2. Math. Dept., Pennsylvania State University, University Park, PA, 16802, USA

    Victor Nistor

Authors
  1. Robert Lauter
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  2. Victor Nistor
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Editor information

Editors and Affiliations

  1. Korteweg-de Vries Instituut voor Wiskunde, Universiteit van Amsterdam, Plantage Muidergracht 24, 1018 TV, Amsterdam, The Netherlands

    N. P. Landsman

  2. Mathematisch-Naturwissenschaftliche Fakultät II Institut für Mathematik, Humboldt-Universität zu Berlin, Unter den Linden 6, 10099, Berlin, Germany

    M. Pflaum

  3. Fakultät für Mathematik und Informatik, Universität Mannheim, D7, 27, 68131, Mannheim, Germany

    M. Schlichenmaier

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Lauter, R., Nistor, V. (2001). Analysis of geometric operators on open manifolds: A groupoid approach. In: Landsman, N.P., Pflaum, M., Schlichenmaier, M. (eds) Quantization of Singular Symplectic Quotients. Progress in Mathematics, vol 198. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8364-1_8

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  • DOI: https://doi.org/10.1007/978-3-0348-8364-1_8

  • Publisher Name: Birkhäuser, Basel

  • Print ISBN: 978-3-0348-9535-4

  • Online ISBN: 978-3-0348-8364-1

  • eBook Packages: Springer Book Archive

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