Controlled Analytic Properties and the Quantitative Baum-Connes Conjecture
Abstract
We show that the classical Baum-Connes assembly map is quantitatively an isomorphism for a class of lacunary hyperbolic groups, and we explain how to see that this class contains many examples of groups that contain graph sequences of large girth inside their Cayley graphs and therefore do not have property (A). This includes the known counterexamples to the Baum-Connes conjecture with coefficients, as well as many other monster groups that have property (T).
Keywords
Cite
@article{arxiv.1908.02131,
title = {Controlled Analytic Properties and the Quantitative Baum-Connes Conjecture},
author = {Martin Finn-Sell},
journal= {arXiv preprint arXiv:1908.02131},
year = {2026}
}
Comments
There is an argument missing for norm control in the K-theory component - it has been known a while but I have only now gotten to it. The representation theory component remains sound. An update will be worked on, but given the delay in this it might take a while. Please feel free to email me and we can discuss if necessary