论文标题
马尔可夫和Roe-Elgebraic方法是渐近扩张的方法
A Markovian and Roe-algebraic approach to asymptotic expansion in measure
论文作者
论文摘要
在本文中，我们对渐近扩展的几何和分析特性进行了进一步的研究。更确切地说，我们开发了马尔可夫扩展的机械，并获得了渐近扩展动作的相关结构。基于此，我们根据Druţu-Nowak投影和相关翘曲锥的ROE代数建立了渐近扩张的分析表征。作为应用程序，我们为粗糙的Baum-Connes猜想提供了新的反例。
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.
