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arXiv · 2008.12572

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

Kang Li·Federico Vigolo·Jiawen Zhang
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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 Dru\c{t}u-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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Kang Li, Federico Vigolo, Jiawen Zhang. 2020-08-28. A Markovian and Roe-algebraic approach to asymptotic expansion in measure. https://arxiv.org/abs/2008.12572

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