Combinatorial aspects of the dual approach to Coxeter and Artin groups
Hot Topics: Artin Groups and Arrangements - Topology, Geometry, and Combinatorics March 11, 2024 - March 15, 2024
Location: SLMath: Eisenbud Auditorium, Online/Virtual
Artin groups
braid groups
Coxeter groups
reflection groups
Garside structures
classifying spaces
hyperplane arrangements
subspace arrangements
configuration spaces
geometric group theory
Matroids
cohomology
The dual approach to Coxeter and Artin groups and the use of Garside theory has successfully been applied to Artin groups of spherical and of affine type. In the study of the Artin groups of affine type first Digne relaxed the condition that the set of atoms of a Garside structure has to be finite, then McCammond-Sulway and Paolini-Salvetti overcame for the affine type the restriction that the set of atoms has to form a lattice with respect to the given order relation.
In the talk I will propose a systematic study of the possible set of atoms in a Coxeter group or in an extended Weyl group, as well of the related monoids and groups.