The p-harmonic boundary for finitely generated groups and the first reduced ℓ_p-cohomology

2007/09/19 by Puls, Michael
#20F65 #31C20 #43A15 #60J50 #FOS: Mathematics #Functional Analysis (math.FA) #Group Theory (math.GR)

paper · doi:10.48550/arxiv.0709.2941

Abstract

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 ℓ^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 ℓ^p-cohomology of G.

Related

• Graphs of bounded degree and the p-harmonic boundary
• The first L^p-cohomology of some finitely generated groups and p-harmonic functions
• Dimensions of l^p-cohomology groups
• The first L^p-cohomology of some groups with one end
• Group cohomology and L^p-cohomology of finitely generated groups