Hecke对的粗糙几何和baum - connes猜想

Pub Date : 2021-12-19 DOI:10.2140/pjm.2023.322.21

Cl'ement Dell'Aiera

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引用次数: 0

摘要

我们利用Hecke对的协集空间及其Schlichting补全的粗糙几何来研究Hecke对。我们证明了Baum-Connes猜想和Novikov猜想在共haagerup情况下的新的稳定性结果。这允许推广以前的结果，同时提供新的例子群满足Baum-Connes猜想与系数。例如，我们证明了对于Sp(5,1)和Sp(3,1)的一些s算术子群，带系数猜想成立。

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Coarse geometry of Hecke pairs and the Baum–Connes conjecture

We study Hecke pairs using the coarse geometry of their coset space and their Schlichting completion. We prove new stability results for the Baum-Connes and the Novikov conjectures in the case where the pair is co-Haagerup. This allows to generalize previous results, while providing new examples of groups satisfying the Baum-Connes conjecture with coefficients. For instance, we show that for some S-arithmetic subgroups of Sp(5,1) and Sp(3,1) the conjecture with coefficients holds.

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