Abstract
In this paper, it is shown that the reduced ℓ p -cohomology is trivial for a class of finitely generated amenable groups called transport amenable. These groups are those for which there exists a sequence of measures ξ n converging to a left-invariant mean and such that the transport cost between ξ n displaced by multiplication on the right by a fixed element and ξ n is bounded (uniformly in n). This class contains groups with controlled Fø lner sequences (such as polycyclic groups) as well as some wreath products (such as H ' ≀ H where H is finitely generated Abelian and the ‘lamp state’ group H ' is finitely generated amenable).
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