2018/01/18 by Benameur, Moulay-Tahar, Roy, Indrava · 1 citation
#FOS: Mathematics #K-Theory and Homology (math.KT) #Operator Algebras (math.OA)
paper · doi:10.48550/arxiv.1801.06040
We introduce the dual Roe algebras for proper étale 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.