4 citations · 6 across the 7 of their papers we have counts for
10 papers
Lie groupoids, pseudodifferential calculus and index theory
Claire Debord, Georges Skandalis
Alain Connes introduced the use of Lie groupoids in noncommutative geometry in his pioneering work on the index theory of foliations. In the present paper, we recall the basic noti…
Blowup constructions for Lie groupoids and a Boutet de Monvel type calculus
Claire Debord, Georges Skandalis
We present natural and general ways of building Lie groupoids, by using the classical procedures of blowups and of deformations to the normal cone. Our constructions are seen to re…
Stability of Lie groupoid C*-algebras
Claire Debord, Georges Skandalis
In this paper we generalize a theorem of M. Hilsum and G. Skandalis stating that the - algebra of any foliation of non zero dimension is stable. Precisely, we show that the C*…
Pseudodifferential extensions and adiabatic deformation of smooth groupoid actions
Claire Debord, Georges Skandalis
The adiabatic groupoid of a smooth groupoid is a deformation relating with its algebroid. In a previous work, we constructed a natura…
Adiabatic groupoid, crossed product by and Pseudodifferential calculus
Claire Debord, Georges Skandalis
We consider the crossed product by of the adiabatic groupoid associated with any Lie groupoid . We construct an explicit Morita equivalence between the exact s…
Pseudodifferential operators on manifolds with fibred corners
Claire Debord, Jean-Marie Lescure, Frédéric Rochon
One way to geometrically encode the singularities of a stratified pseudomanifold is to endow its interior with an iterated fibred cusp metric. For such a metric, we develop and stu…