Ribbons in Garside monoids

TL;DR

This paper explores the properties of ribbons within Garside monoids, providing a unified framework that includes spherical Artin monoids and dual braid monoids of complex reflection groups.

Contribution

It generalizes existing results on parabolic subgroups to a broader setting of Garside monoids, encompassing various classes of braid and Artin groups.

Findings

Unified framework for ribbons in Garside monoids

Generalization of parabolic subgroup results

Applicable to spherical Artin and dual braid monoids

Abstract

We expound the properties of ribbons in a setting which is general enough to encompass spherical Artin monoids and dual braid monoids of well-generated complex reflection groups. We generalize to our setting results on parabolic subgroups of spherical Artin group of Godelle, Cumplido, and others.