1 citations · 1 across the 7 of their papers we have counts for
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Generalized J-groups, J-braid groups and Seifert link groups
Owen Garnier, Igor Haladjian
The family of J-groups was introduced by Achar and Aubert with the goal of providing Coxeter-like combinatorial tools for studying rank 2 complex reflection groups. However, J-grou…
Conjugacy invariants and rigidity in Garside groups: a uniformity phenomenon
Matthieu Calvez, Owen Garnier, Juan González-Meneses +1
Consider an element~ of a Garside group which is rigid in the sense of Garside-theory. Let be the set of rigid conjugates of~ -- this is a well-known characteristic s…
Normalisers of parabolic subgroups of Artin--Tits groups and Tits cone intersections
Owen Garnier, Edmund Heng, Anthony Licata +1
Let be a Coxeter diagram and let . Motivated by 3-fold flops, Iyama and Wemyss study the hyperplane arrangement in the Tits cone intersection of , which is a…
Proof of Shvartsman's conjecture on braid groups of projective complex reflection groups
Owen Garnier
The purpose of this note is to prove a conjecture of Shvartsman relating a complex projective reflection group with the quotient of a suitable complex braid group by its center. Sh…
Parabolic subgroups of complex braid groups: the remaining case
Owen Garnier
Recently, Marin and González-Meneses introduced a class of ``parabolic'' subgroups for generalized braid groups associated to arbitrary complex reflection groups. Using notably Gar…
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…
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…
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…
Regular theory in complex braid groups
Owen Garnier
In his seminal paper on complex reflection arrangements, Bessis introduces a Garside structure for the braid group of a well-generated irreducible complex reflection group. Using t…