$\ell^p$ -上同调的消失与运输成本
Vanishing of $\ell^p$-cohomology and transportation cost
摘要：
本文证明了对于一类称为迁移顺从的可生成顺从群，约化的$\ell^p$ -上同调是平凡的.这些组是那些存在一个序列的措施$ξ_n$收敛到一个左不变的平均值，并使运输成本之间的$ξ_n$取代由一个固定的元素在右边的乘法和$ξ_n$是有界的$n$。该类包含具有受控Følner序列的群（如多圈群）以及某些圈积。注意事项：例5.1和5.2不正确（特别是$\mathbb{Z} \wr \mathbb{Z}$和$(\mathbb{Z}/2\mathbb{Z})\wr \mathbb{Z}^2$不适合运输）;本版本附有勘误表和附录。
英文摘要：
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. Note: Examples 5.1 and 5.2 are incorrect (in particular $\mathbb{Z} \wr \mathbb{Z}$ and $(\mathbb{Z}/2\mathbb{Z})\wr \mathbb{Z}^2$ are not transport amenable); an erratum and addendum is appended to this version.
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