English

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}
}