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

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.

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Cited by in corpus (2)

• Asymptotic expansion in measure and strong ergodicity
• On the structure of asymptotic expanders