Bounded cohomology of amenable covers via classifying spaces

TL;DR

This paper provides an alternative proof for the bounded cohomology of amenable covers using classifying spaces, extending Gromov and Ivanov's work on cohomology of contractible covers.

Contribution

It introduces a new proof method leveraging classifying spaces of subgroup families for bounded cohomology of amenable covers.

Findings

Alternative proof of Gromov and Ivanov's theorem

Utilizes classifying spaces to analyze bounded cohomology

Enhances understanding of amenable covers in bounded cohomology

Abstract

Gromov and Ivanov established an analogue of Leray's theorem on cohomology of contractible covers for bounded cohomology of amenable covers. We present an alternative proof of this fact, using classifying spaces of families of subgroups.