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arXiv · 2112.10120

Coarse geometry of Hecke pairs and the Baum-Connes conjecture

Clément Dell'Aiera
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Abstract

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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Clément Dell'Aiera. 2021-12-19. Coarse geometry of Hecke pairs and the Baum-Connes conjecture. https://doi.org/10.2140/pjm.2023.322.21

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