5 papers
Smallest quotients and profinite rigidity of irreducible spherical type Artin groups
Federica Gavazzi, Igor Haladjian, Luis Paris
We prove that irreducible spherical type Artin groups are profinitely rigid within the class of all spherical type Artin groups. As part of the proof, building on ideas of Kolay fo…
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…
J-braid groups are torus necklace groups
Igor Haladjian
We construct a family of links we call torus necklaces for which the link groups are precisely the braid groups of generalised -reflection groups. Moreover, this correspondence…
Braid groups of J-reflection groups and associated classical and dual Garside structures
Igor Haladjian
The family of -reflection groups can be seen as a combinatorial generalisation of irreducible rank two complex reflection groups and was introduced by the author in a previous a…
A Combinatorial Generalisation of Rank two Complex Reflection Groups via Generators and Relations
Igor Haladjian
Complex reflection groups of rank two are precisely the finite groups in the family of groups that we call J-reflection groups. These groups are particular cases of J-groups as def…