l^p-cohomology for groups of type FP_n

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

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.

The first $L^p$-cohomology of some finitely generated groups and $p$-harmonic functions

Let $G$ be a finitely generated infinite group and let $p > 1$. In this paper we make a connection between the first $L^p$-cohomology space of $G$ and $p$-harmonic functions on $G$. We also describe the elements in the first $L^p$-cohomology space of groups with polynomial growth, and we give an inclusion result for nonamenable groups.

The first $L^p$-cohomology of some groups with one end

Let $p$ be a real number greater than one. In this paper we study the vanishing and nonvanishing of the first $L^p$-cohomology space of some groups that have one end. We also make a connection between the first $L^p$-cohomology space and the Floyd boundary of the Cayley graph of a group. We apply the result about Floyd boundaries to show that there exists a real number $p$ such that the first $L^p$-cohomology space of a nonelementary hyperbolic group does not vanish.

测度群胚的可测有界上同调

Measurable bounded cohomology of measured groupoids

本文为测度群胚引入可测有界上同调理论，证明其同构于局部紧群的连续有界上同调，并揭示在轨道等价与测度等价下的不变性及顺从群胚的平凡性。

Group 1-cohomology is complemented

We show a structural property of cohomology with coefficients in an isometric representation on a uniformly convex Banach space: if the cohomology group $H^1(G,π)$ is reduced, then, up to an isomorphism, it is a closed complemented, subspace of the space of cocycles and its complement is the subspace of coboundaries.

On the l^{q,p} cohomology of Carnot groups

We study the simplicial {\ell} q,p cohomology of Carnot groups G. We show vanishing and non-vanishing results depending of the range of the (p, q) gap with respect to the weight gaps in the Lie algebra cohomology of G.