Aut-invariant word norm on right angled Artin and right angled Coxeter groups

TL;DR

This paper demonstrates that the Aut-invariant word norm on right-angled Artin and Coxeter groups is generally unbounded, providing characteristic subgroups and unbounded quasimorphisms to establish this property.

Contribution

The paper introduces a method to prove unboundedness of the Aut-invariant word norm using characteristic subgroups and constructs unbounded quasimorphisms.

Findings

Aut-invariant word norm is unbounded in most cases

Existence of characteristic subgroups facilitating the proof

Construction of Lipschitz unbounded quasimorphisms

Abstract

We show that the Aut-invariant word norm on right angled Artin and right angled Coxeter groups is unbounded (except in few special cases). To prove unboundedness we exhibit certain characteristic subgroups. This allows us to find unbounded quasimorphisms which are Lipschitz with respect to the Aut-invariant word norm.