Boyd, R. , Charney, R., Morris-Wright, R. and Rees, S. (2024) The Artin monoid Cayley graph. Journal of Combinatorial Algebra, (doi: 10.4171/JCA/85) (Early Online Publication)
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Abstract
In this paper, we investigate properties of the Artin monoid Cayley graph. This is the Cayley graph of an Artin group A Γ with respect to the (infinite) generating set given by the associated Artin monoid A +/Γ. 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 AΓ 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.
Item Type: | Articles |
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Keywords: | Artin monoids, Artin groups. |
Status: | Early Online Publication |
Refereed: | Yes |
Glasgow Author(s) Enlighten ID: | Boyd, Dr Rachael |
Authors: | Boyd, R., Charney, R., Morris-Wright, R., and Rees, S. |
College/School: | College of Science and Engineering > School of Mathematics and Statistics > Mathematics |
Journal Name: | Journal of Combinatorial Algebra |
Publisher: | EMS Press |
ISSN: | 2415-6302 |
ISSN (Online): | 2415-6302 |
Copyright Holders: | Copyright: © 2024 EMS Press |
First Published: | First published in Journal of Combinatorial Algebra 2024 |
Publisher Policy: | Reproduced in accordance with the publisher copyright policy |
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