Coarse geometry of Hecke pairs and the Baum-Connes conjecture
K-Theory and Homology
2023-05-03 v2 Algebraic Topology
Operator Algebras
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.
Keywords
Cite
@article{arxiv.2112.10120,
title = {Coarse geometry of Hecke pairs and the Baum-Connes conjecture},
author = {Clément Dell'Aiera},
journal= {arXiv preprint arXiv:2112.10120},
year = {2023}
}