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

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

2002-04-17

arxiv.org/abs/math/0204220v1

Mathematics

Functional Analysis

Accepted Canadian Mathematical Bulletin

Scientific paper

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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