有限生成群的p-调和边界与第一约化\ell_p -上同调
The p-harmonic boundary for finitely generated groups and the first reduced \ell_p-cohomology
摘要：
设$p$是一个大于1的实数，$G$是一个随机生成的无限群。本文引入了$G$的$p$ -调和边界.然后，我们的特点消失的第一个减少$\ell^p$上同调的$G$在这个边界的基数。给出了在粗糙等距下保持的$p$ -调和边界的一些性质。研究了$G$上的平移不变线性泛函、$G$的$p$ -调和边界和$G$的第一约化$\ell^p$ -上同调之间的关系.
英文摘要：
Let $p$ be a real number greater than one and let $G$ be a finitely generated, infinite group. In this paper we introduce the $p$-harmonic boundary of $G$. We then characterize the vanishing of the first reduced $\ell^p$-cohomology of $G$ in terms of the cardinality of this boundary. Some properties of $p$-harmonic boundaries that are preserved under rough isometries are also given. We also study the relationship between translation invariant linear functionals on a certain difference space of functions on $G$, the $p$-harmonic boundary of $G$ and the first reduced $\ell^p$-cohomology of $G$.
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