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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…