Controlled Analytic Properties and the Quantitative Baum-Connes\n Conjecture

2019/08/06 by Martin Finn-Sell, Finn-Sell, Martin
Computer Science · Mathematics · #Advanced Operator Algebra Research #FOS: Mathematics #Geometric and Algebraic Topology #Group Theory (math.GR) #Holomorphic and Operator Theory #K-Theory and Homology (math.KT) #Mathematical Dynamics and Fractals #Operator Algebras (math.OA) #Topological and Geometric Data Analysis

paper · pdf · doi:10.48550/arxiv.1908.02131

openalex publication_date 2019/08/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that the classical Baum-Connes assembly map is quantitatively an\nisomorphism for a class of lacunary hyperbolic groups, and we explain how to\nsee that this class contains many examples of groups that contain graph\nsequences of large girth inside their Cayley graphs and therefore do not have\nproperty (A). This includes the known counterexamples to the Baum-Connes\nconjecture with coefficients, as well as many other monster groups that have\nproperty (T).\n

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