## The Michigan Mathematical Journal

### Aut-Invariant Word Norm on Right-Angled Artin and Right-Angled Coxeter Groups

Michał Marcinkowski

#### Abstract

We prove that the $\mathrm{Aut}$-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 quasi-morphisms which are Lipschitz with respect to the $\mathrm{Aut}$-invariant word norm.

#### Article information

Source
Michigan Math. J., Advance publication (2020), 11 pages.

Dates
Revised: 7 August 2018
First available in Project Euclid: 16 November 2019

https://projecteuclid.org/euclid.mmj/1573873440

Digital Object Identifier
doi:10.1307/mmj/1573873440

Subjects
Primary: 51 20

#### Citation

Marcinkowski, Michał. Aut-Invariant Word Norm on Right-Angled Artin and Right-Angled Coxeter Groups. Michigan Math. J., advance publication, 16 November 2019. doi:10.1307/mmj/1573873440. https://projecteuclid.org/euclid.mmj/1573873440

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