Adiabatic groupoid, crossed product by \R₊^* and Pseudodifferential calculus

2013/07/24 by Claire Debord, Debord, Claire, Georges Skandalis +1 · 3 citations
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #Functional Analysis (math.FA) #math.DG #math.FA

paper · pdf · doi:10.48550/arxiv.1307.6320

arxiv created 2013/10/09 · arxiv updated 2013/10/10

Abstract

We consider the crossed product G_ga by \R₊^* of the adiabatic groupoid associated with any Lie groupoid G. We construct an explicit Morita equivalence between the exact sequence of order 0 pseudodifferential operators on G and (a restriction of) the natural exact sequence associated with G_ga. As an important intermediate step, we express a pseudodifferential operator on G as an integral associated to a smoothing operator on the adiabatic groupoid G_ad of G.

Cited by

• Sharp mapping properties of Poisson transforms and the Baum-Connes conjecture
• A Volterra Calculus for Lie Groupoids
• Extensions of homogeneous distributions on deformations to the normal cone

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