Aut-invariant quasimorphisms on graph products of abelian groups

TL;DR

This paper constructs automorphism-invariant unbounded quasimorphisms for certain graph products of abelian groups, including right-angled Artin and Coxeter groups, and explores their geometric and algebraic properties.

Contribution

It introduces new automorphism-invariant quasimorphisms for graph products of abelian groups, extending the understanding of their algebraic and geometric structures.

Findings

Existence of unbounded automorphism-invariant quasimorphisms

Application to right-angled Artin and Coxeter groups

Non-triviality of an invariant stable commutator length analogue

Abstract

The present paper constructs unbounded quasimorphisms that are invariant under all automorphisms on free products of more than two factors and on graph products of finitely generated abelian groups. This includes many classes of right angled Artin and right angled Coxeter groups. We discuss various geometrically arising families of graphs as examples and deduce the non-triviality of an invariant analogue of stable commutator length recently introduced by Kawasaki and Kimura for these groups.