Adiabatic groupoid, crossed product by \(\mathbb R_+^\ast\) and pseudodifferential calculus

DOI10.1016/j.aim.2014.02.012zbMath1300.58007arXiv1307.6320OpenAlexW1976500442MaRDI QIDQ2445849

Claire Debord, Georges Skandalis

Publication date: 15 April 2014

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1307.6320

zbMATH Keywords

noncommutative geometrygroupoidspseudodifferential calculus

Mathematics Subject Classification ID

Topological groupoids (including differentiable and Lie groupoids) (22A22) Pseudogroups and differentiable groupoids (58H05)

Related Items (30)

Stability of Lie groupoid \(C^\ast\)-algebras ⋮ Analysis on singular spaces: Lie manifolds and operator algebras ⋮ A general Simonenko local principle and Fredholm condition for isotypical components ⋮ Double layer potentials on polygons and pseudodifferential operators on Lie groupoids ⋮ Analytic torsion of generic rank two distributions in dimension five ⋮ Pseudodifferential extensions and adiabatic deformation of smooth groupoid actions ⋮ Pseudodifferential operators on filtered manifolds as generalized fixed points ⋮ Reflexivity of the space of transversal distributions ⋮ Lie groupoid deformations and convolution algebras ⋮ Boutet de Monvel operators on singular manifolds ⋮ Pseudo-differential extension for graded nilpotent Lie groups ⋮ A pseudodifferential analytic perspective on Getzler's rescaling ⋮ A groupoid approach to the Wodzicki residue ⋮ Hypoelliptic operators in geometry. Abstracts from the workshop held May 21--26, 2023 ⋮ Analysis, geometry and topology of singular PDE. Abstracts from the workshop held June 6--12, 2021 (hybrid meeting) ⋮ Complex quantum groups and a deformation of the Baum–Connes assembly map ⋮ The Baum–Connes conjecture: an extended survey ⋮ Lie groupoids, pseudodifferential calculus, and index theory ⋮ Tangent maps and tangent groupoid for Carnot manifolds ⋮ Lie groupoids, exact sequences, Connes-Thom elements, connecting maps and index maps ⋮ Double layer potentials on three-dimensional wedges and pseudodifferential operators on Lie groupoids ⋮ Boutet de Monvel operators on Lie manifolds with boundary ⋮ The Fredholm property for groupoids is a local property ⋮ A Baum-Connes conjecture for singular foliations ⋮ The heat asymptotics on filtered manifolds ⋮ Fredholm Conditions on Non-compact Manifolds: Theory and Examples ⋮ The adiabatic groupoid and the Higson-Roe exact sequence ⋮ On the deformation groupoid of the inhomogeneous pseudo‐differential Calculus ⋮ Graded hypoellipticity of BGG sequences ⋮ A groupoid approach to pseudodifferential calculi

Cites Work

• Factorization in group algebras
• Boutet de Monvel's calculus and groupoids. I.
• Factorization in \(C^*\)-algebras
• A groupoid approach to C*-algebras
• Equivariant Kasparov theory and groupoids. I
• Pseudodifferential operators on differential groupoids
• Operator theory in the \(C^*\)-algebra framework
• Continuous family groupoids
• Pseudodifferential analysis on continuous family groupoids
• Lie groupoids, exact sequences, Connes-Thom elements, connecting maps and index maps
• Groupoids and pseudodifferential calculus on manifolds with corners
• Functional calculus of pseudodifferential boundary problems.
• Unbounded pseudodifferential calculus on Lie groupoids
• Index theory and Groupoids
• The analytic index of elliptic pseudodifferential operators on a singular foliation
• A Schwartz type algebra for the Tangent Groupoid
• The holonomy groupoid of a singular foliation
• Elliptic symbols, elliptic operators and Poincaré duality on conical pseudomanifolds
• Morphismes $K$-orientés d'espaces de feuilles et fonctorialité en théorie de Kasparov (d'après une conjecture d'A. Connes)
• Pseudodifferential calculus on manifolds with corners and groupoids
• Indice analytique et groupoïdes de Lie
• Regular representation of groupoid C* -algebras and applications to inverse semigroups
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Adiabatic groupoid, crossed product by \(\mathbb R_+^\ast\) and pseudodifferential calculus