On Asymptotic and Continuous Group Orlicz Cohomology

TL;DR

This paper extends results on asymptotic and continuous group cohomology from L^p spaces to Orlicz spaces, establishing invariance properties and analyzing the degree one case in detail.

Contribution

It introduces the concept of Orlicz cohomology for groups, proving invariance under quasi-isometries and exploring the degree one case.

Findings

Asymptotic Orlicz cohomology is a quasi-isometry invariant.

Both asymptotic and continuous Orlicz cohomology coincide for certain groups.

Degree one case is analyzed in detail.

Abstract

We generalize some results on asymptotic and continuous group $L^p$-cohomology to Orlicz cohomology. In particular, we show that asymptotic Orlicz cohomology is a quasi-isometry invariant and that both notions coincide in the case of a locally compact second countable group. The case of degree $1$ is studied in more detail.