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Article Dans Une Revue Journal of Noncommutative Geometry Année : 2019

The Higson-Roe sequence for etale groupoids. I. Dual algebras and compatibility with the BC map

Résumé

We introduce the dual Roe algebras for proper \'{e}tale groupoid actions and deduce the expected Higson-Roe short exact sequence. When the action is cocompact, we show that the Roe $C^*$-ideal of locally compact operators is Morita equivalent to the reduced $C^*$-algebra of our groupoid, and we further identify the boundary map of the associated periodic six-term exact sequence with the Baum-Connes map, via a Paschke-Higson map for groupoids. For proper actions on continuous families of manifolds of bounded geometry, we associate with any $G$-equivariant Dirac-type family, a coarse index class which generalizes the Paterson index class and also the Moore-Schochet Connes' index class for laminations.

Dates et versions

hal-01819123 , version 1 (20-06-2018)

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Moulay Tahar Benameur, Indrava Roy. The Higson-Roe sequence for etale groupoids. I. Dual algebras and compatibility with the BC map. Journal of Noncommutative Geometry, In press, ⟨10.4171/JNCG/358⟩. ⟨hal-01819123⟩
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