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math.GR2023★ 1 cited
Uniqueness of roots up to conjugacy in circular and hosohedral-type Garside groups
Owen Garnier
We consider a particular class of Garside groups, which we call circular groups. We mainly prove that roots are unique up to conjugacy in circular groups. This allows us to complet…
math.GR2023
Springer categories for regular centralizers in well-generated complex braid groups
Owen Garnier
In his proof of the K(pi,1) conjecture for complex reflection arrangements, Bessis defined Garside categories suitable for studying braid groups of centralizers of Springer regular…
math.GR2023
Generalization of the Dehornoy-Lafont order complex to categories. Application to exceptional braid groups
Owen Garnier
The homology of a Garside monoid, thus of a Garside group, can be computed efficiently through the use of the order complex defined by Dehornoy and Lafont. We construct a categoric…