Nikolaus Conference 2019

Speaker: Georges Neaime (Bielefeld)

Title: Interval Garside Structures Related to Artin Groups and Their Generalizations

Abstract:

A Garside group is realized as the group of fractions of a monoid, called a Garside monoid, in which there exist divisibility relations that provide relevant information about the Garside group. Garside groups enjoy many remarkable group-theoretical, homological, and homotopical properties. Interval Garside structures are Garside monoids and groups that can be constructed from lattices in a given group. Garside theory applies to some families of Artin groups and to the complex braid groups attached to irreducible complex reflection groups. The classical and dual approaches are two standard approaches in order to possibly construct interval Garside structures for these groups. In this talk, combining both classical and dual approaches, I will construct interval Garside structures for the affine Artin groups of type \(\tilde{A}\) and for the complex braid groups of type \((e,e,n)\).

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