A Markovian and Roe-algebraic approach to asymptotic expansion in measure

2020/08/28 by Kang Li, Li, Kang, Federico Vigolo +3 · 2 citations
Mathematics · #19K56 #37A15 #37A30 #46H35 #Advanced Banach Space Theory #Advanced Operator Algebra Research #Advanced Topics in Algebra #Dynamical Systems (math.DS) #FOS: Mathematics #Operator Algebras (math.OA)

paper · pdf · doi:10.48550/arxiv.2008.12572

openalex publication_date 2020/08/28 · openalex created_date 2020/09/08 · openalex updated_date 2026/07/28

Abstract

In this paper, we conduct further studies on geometric and analytic properties of asymptotic expansion in measure. More precisely, we develop a machinery of Markov expansion and obtain an associated structure theorem for asymptotically expanding actions. Based on this, we establish an analytic characterisation for asymptotic expansion in terms of the Druţu-Nowak projection and the Roe algebra of the associated warped cones. As an application, we provide new counterexamples to the coarse Baum-Connes conjecture.

Citations

• Quasi-local Algebras and Asymptotic Expanders

Cited by

• Coarse cone quotients
• Asymptotic expansion for groupoids and Roe type algebras

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