Slowness of residually finite amenable groups

Determine whether every residually finite amenable group is slow in the sense of Bridson–Kochloukova (i.e., satisfies their slowness condition implying vanishing homology growth).

Background

The authors relate their algebraic cheap domination property to the geometric notion of “slowness” introduced by Bridson–Kochloukova, which implies vanishing homology growth.

They note that it is unknown whether residually finite amenable groups satisfy slowness, despite strong vanishing results for torsion homology growth obtained via their algebraic framework.