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

Abstract

Let $G$ be a finitely generated, infinite group, let $p>1$, and let $L^p(G)$ denote the Banach space $\{{\sum }_{x\in G}{a}_{x}x\mid {\sum }_{x\in G}|a_x{|}^p<\infty \}$. 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.

Accepted Canadian Mathematical Bulletin