Bushy pseudocharacters and group actions on quasi-trees

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. Contents 1. Introduction 1 2. Actions and pseudocharacters 3 3. Existence of bushy pseudocharacters 8 4. Quasi-actions on trees 10 5. Space of pseudocharacters 11 References 13