K-theory for the maximal Roe algebra of certain expandersReport as inadecuate

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* Corresponding author 1 PIMS - Pacific Institut for Mathematical Sciences 2 LMBP - Laboratoire de Mathématiques Blaise Pascal 3 Department of Mathematics, Vanderbilt University

Abstract : We study in this paper the maximal version of the coarse Baum-Connes assembly map for families of expanding graphs arising from residually finite groups. Unlike for the usual Roe algebra, we show that this assembly map is closely related to the maximal Baum-Connes assembly map for the group and is an isomorphism for a class of expanders. We also introduce a quantitative Baum-Connes assembly map and discuss its connections to K-theory of maximal Roe algebras.

Keywords : Baum-Connes Conjecture Coarse Geometry Expanders Novikov Conjecture Operator Algebra K-theory Roe Algebras

Author: Hervé Oyono-Oyono - Guoliang Yu -

Source: https://hal.archives-ouvertes.fr/


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