Groupoids and pseudodifferential calculus on manifolds with corners

We associate to any manifold with corners (even with non-embedded hyperfaces) a (non-Hausdorff) longitudinally smooth Lie groupoid, on which we define a pseudodifferential calculus. This calculus generalizes the b-calculus of Melrose, defined for manifolds with embedded corners. The groupoid of a ma...

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Bibliographic Details
Published in:Journal of functional analysis 2003-04, Vol.199 (1), p.243-286
Main Author: Monthubert, Bertrand
Format: Article
Language:English
Subjects:
[formula omitted]-algebras
Differentiable groupoids
Index theory
Manifolds with corners
Pseudodifferential calculus
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Summary:We associate to any manifold with corners (even with non-embedded hyperfaces) a (non-Hausdorff) longitudinally smooth Lie groupoid, on which we define a pseudodifferential calculus. This calculus generalizes the b-calculus of Melrose, defined for manifolds with embedded corners. The groupoid of a manifold with corners is shown to be unique up to equivalence for manifolds with corners of same codimension. Using tools from the theory of C ∗ -algebras of groupoids, we also obtain new proofs for the study of b-calculus.
ISSN:0022-1236
1096-0783
DOI:10.1016/S0022-1236(02)00038-1