Bushy pseudocharacters and group actions on quasi-trees

TL;DR

This paper investigates conditions under which pseudocharacters are bushy in groups acting on quasi-trees, linking these conditions to bounded cohomology and expanding understanding of pseudocharacter spaces.

Contribution

It provides sufficient conditions for bushy pseudocharacters in groups acting on quasi-trees, connecting with bounded cohomology theories.

Findings

Identifies conditions for bushy pseudocharacters

Relates pseudocharacters to bounded cohomology

Analyzes the structure of pseudocharacter spaces

Abstract

Given a group acting on a graph quasi-isometric to a tree, we give sufficent conditions for a pseudocharacter to be bushy. We relate this with the conditions studied by M. Bestvina and K. Fujiwara on their work on bounded cohomology and obtain some results on the space of pseudocharacters.