The adiabatic groupoid and the Higson-Roe exact sequence

2019/01/15 by Zenobi, Vito Felice · 1 citation
#19K56 #22A22 #46L80 #FOS: Mathematics #K-Theory and Homology (math.KT) #Operator Algebras (math.OA)

paper · doi:10.48550/arxiv.1901.05081

Abstract

Let \widetildeX be a smooth Riemannian manifold equipped with a proper, free, isometric and cocompact action of a discrete group Γ. In this paper we prove that the analytic surgery exact sequence of Higson-Roe for \widetildeX is isomorphic to the exact sequence associated to the adiabatic deformation of the Lie groupoid \widetildeX×_Γ\widetildeX. We then generalize this result to the context of smoothly stratified manifolds. Finally, we show, by means of the aforementioned isomorphism, that the \varrho-classes associated to a metric with positive scalar curvature defined by Piazza and Schick corresponds to the \varrho-classes defined by the author of this paper.

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