ePrints

The Artin monoid Cayley graph

Lookup NU author(s): Professor Sarah Rees

Downloads

• Published version [.pdf]

Licence

This work is licensed under a Creative Commons Attribution 4.0 International License (CC BY 4.0).

Abstract

© 2024 European Mathematical Society.In this paper, we investigate properties of the Artin monoid Cayley graph. This is the Cayley graph of an Artin group A with respect to the (infinite) generating set given by the associated Artin monoid AC . In a previous paper, the first three authors introduced a monoid Deligne complex and showed that this complex is contractible for all Artin groups. In this paper, we show that the Artin monoid Cayley graph is quasi-isometric to a modification of the Deligne complex for A obtained by coning off translates of the monoid Deligne complex. We then address the question of when the monoid Cayley graph has infinite diameter. We conjecture that this holds for all Artin groups of infinite type. We give a set of criteria that imply infinite diameter, and using existing solutions to the word problem for large type Artin groups and 3-free Artin groups, we prove that the conjecture holds for any Artin group containing a 3-generator subgroup of one of these two types.

Publication metadata

Author(s): Boyd R, Charney R, Morris-Wright R, Rees S

Publication type: Article

Publication status: Published

Journal: Journal of Combinatorial Algebra

Year: 2026

Volume: 10

Issue: 1-2

Pages: 131-151

Online publication date: 10/01/2024

Acceptance date: 21/09/2023

Date deposited: 30/03/2026

ISSN (print): 2415-6302

ISSN (electronic): 2415-6310

Publisher: European Mathematical Society Publishing House

URL: https://doi.org/10.4171/JCA/85

DOI: 10.4171/JCA/85

Altmetrics

Funding

Share