The Artin monoid Cayley graph

Rachael BoydRuth CharneyRose Morris-WrightSarah Rees

Mar 2023

摘要

In this paper we investigate properties of the Artin monoid Cayley graph.This is the Cayley graph of an Artin group $A_\Gamma$ with respect to the(infinite) generating set given by the associated Artin monoid $A^+_\Gamma$. Ina previous paper, the first three authors introduced a monoid Deligne complexand showed that this complex is contractible for all Artin groups. In thispaper, we show that the Artin monoid Cayley graph is quasi-isometric to amodification of the Deligne complex for $A_\Gamma$ obtained by coning offtranslates of the monoid Deligne complex. We then address the question of whenthe monoid Cayley graph has infinite diameter. We conjecture that this holdsfor all Artin groups of infinite type. We give a set of criteria that implyinfinite diameter, and using existing solutions to the word problem forlarge-type Artin groups and 3-free Artin groups, we prove that the conjectureholds for any Artin group containing a 3-generator subgroup of one of these twotypes.

展开全部

图表提取

论文十问

参考文献

被引用

提问与回答

暂无人提供速读十问回答

被引用

笔记

问答

领域