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Group cohomology and $L^p$-cohomology of finitely generated groups

Michael Puls
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Abstract

Let $G$ be a finitely generated, infinite group, let $p>1$, and let $L^p(G)$ denote the Banach space $\{\sum_{x\in G} a_xx \mid \sum_{x\in G} |a_x |^p < \infty \}$. In this paper we will study the first cohomology group of $G$ with coefficients in $L^p(G)$, and the first reduced $L^p$-cohomology space of $G$. Most of our results will be for a class of groups that contains all finitely generated, infinite nilpotent groups.

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Michael Puls. 2002-04-17. Group cohomology and $L^p$-cohomology of finitely generated groups. https://arxiv.org/abs/math/0204220

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