On the arboreal structure of right-angled Artin groups

TL;DR

This paper explores the arboreal structure of right-angled Artin groups within the broader context of median groups, providing new structural theorems and insights into their algebraic properties.

Contribution

It introduces and investigates classes of median groups, especially A-groups, and applies these to systematically analyze the arboreal structure of right-angled Artin groups.

Findings

Structure theorems for foldings and directions

Results on quasidirections and centralizers

Systematic understanding of the arboreal structure

Abstract

The present article continues the study of median groups initiated in [6, 9, 10]. Some classes of median groups are introduced and investigated with a stress upon the class of the so called A-groups which contains as remarkable subclasses the lattice ordered groups and the right-angled Artin groups. Some general results concerning A-groups are applied to a systematic study of the arboreal structure of right-angled Artin groups. Structure theorems for foldings, directions, quasidirections and centralizers are proved.