Expanders are counterexamples to the $\ell^p$ coarse Baum-Connes conjecture

TL;DR

This paper demonstrates that for expanders derived from residually finite hyperbolic groups, the $\,\ell^p$ coarse Baum-Connes assembly map fails to be surjective, providing counterexamples to the conjecture.

Contribution

It introduces counterexamples to the $\,\ell^p$ coarse Baum-Connes conjecture using expanders from hyperbolic groups, highlighting limitations of the conjecture.

Findings

The $\,\ell^p$ assembly map is not surjective for certain expanders.

Expanders from residually finite hyperbolic groups serve as counterexamples.

The results challenge the universality of the $\,\ell^p$ coarse Baum-Connes conjecture.

Abstract

We consider an $\ell^p$ coarse Baum-Connes assembly map for $1<p<\infty$, and show that it is not surjective for expanders arising from residually finite hyperbolic groups.