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arXiv · 1207.0451

Vanishing of $\ell^p$-cohomology and transportation cost

Antoine Gournay
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Abstract

In this paper, it is shown that the reduced $\ell^p$-cohomology is trivial for a class of finitely generated amenable groups called transport amenable. These groups are those for which there exist 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 in $n$. This class contains groups with controlled Følner sequence (such as polycylic groups) as well as some wreath products (such as arbitrary wreath products of finitely generated Abelian groups).

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Antoine Gournay. 2013-04-12. Vanishing of $\ell^p$-cohomology and transportation cost. https://arxiv.org/abs/1207.0451

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