On transfer in bounded cohomology

TL;DR

This paper introduces a transfer map in bounded cohomology with metric G-module coefficients and extends a key comparison theorem to Lie groups with finitely many components.

Contribution

It defines a transfer map in bounded cohomology and generalizes an existing theorem to a broader class of Lie groups.

Findings

Defined a transfer map in bounded cohomology with metric G-module coefficients

Extended the comparison theorem to Lie groups with finitely many connected components

Provided new tools for studying bounded cohomology in Lie group settings

Abstract

We define a transfer map in the setting of bounded cohomology with certain metric G-module coefficients. As an application, we extend a theorem of Chatterji, Mislin, Pittet and Saloff-Coste on the comparison map from Borel-bounded to Borel cohomology, to cover the case of Lie groups with finitely many connected components.