Geodesic
On spectra of geometric operators on open manifolds and differentiable groupoids
Lauter, Robert1 ; Nistor, Victor2
1 Universität Mainz, Fachbereich 17-Mathematik, D-55099 Mainz, Germany
2 Pennsylvania State University, Department of Mathematics, University Park, PA 16802
Electronic research announcements of the American Mathematical Society, Tome 07 (2001), pp. 45-53.

Voir la notice de l'article provenant de la source American Mathematical Society

We use a pseudodifferential calculus on differentiable groupoids to obtain new analytical results on geometric operators on certain noncompact Riemannian manifolds. The first step is to establish that the geometric operators belong to a pseudodifferential calculus on an associated differentiable groupoid. This then leads to Fredholmness criteria for geometric operators on suitable noncompact manifolds, as well as to an inductive procedure to compute their essential spectra. As an application, we answer a question of Melrose on the essential spectrum of the Laplace operator on manifolds with multicylindrical ends.
DOI : 10.1090/S1079-6762-01-00093-2

Lauter, Robert 1 ; Nistor, Victor 2

1 Universität Mainz, Fachbereich 17-Mathematik, D-55099 Mainz, Germany
2 Pennsylvania State University, Department of Mathematics, University Park, PA 16802 
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Lauter, Robert; Nistor, Victor. On spectra of geometric operators on open manifolds and differentiable groupoids. Electronic research announcements of the American Mathematical Society, Tome 07 (2001), pp. 45-53. doi : 10.1090/S1079-6762-01-00093-2. http://geodesic.mathdoc.fr/articles/10.1090/S1079-6762-01-00093-2/

[1] Connes, Alain Sur la théorie non commutative de l’intégration 1979 19 143

[2] Connes, Alain Noncommutative geometry 1994

[3] Melrose, Richard B. Geometric scattering theory 1995

[4] Melrose, Richard B. Fibrations, compactifications and algebras of pseudodifferential operators 1996 246 261

[5] Melrose, Richard B., Piazza, Paolo Analytic 𝐾-theory on manifolds with corners Adv. Math. 1992 1 26

[6] Monthubert, Bertrand, Pierrot, François Indice analytique et groupoïdes de Lie C. R. Acad. Sci. Paris Sér. I Math. 1997 193 198

[7] Monthubert, Bertrand Pseudodifferential calculus on manifolds with corners and groupoids Proc. Amer. Math. Soc. 1999 2871 2881

[8] Nistor, Victor, Weinstein, Alan, Xu, Ping Pseudodifferential operators on differential groupoids Pacific J. Math. 1999 117 152

[9] Renault, Jean A groupoid approach to 𝐶*-algebras 1980

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