Nikolaus Conference 2022

Speaker: Barbara Baumeister (Bielefeld)

Title: The Dual Approach to Coxeter and Artin Groups: Quasi-Coxeter Elements


Garside structures have been key to our understanding of spherical-type Artin groups. A first Garside structure for these groups was found by Brieskorn and Saito. Bessis, Digne and Michel (also Birman, Ko, Lee should be mentioned) started the dual approach to Coxeter and Artin groups to obtain an even nicer Garside structure, and in order to be able to generalise Garside's ideas to infinite Coxeter groups.

In this approach the Coxeter elements play a major role. Coxeter elements are chosen as they satisfy a property that is also satisfied by quasi-Coxeter elements (the Hurwitz-transitivity). In the talk I will present what is happening if we replace a Coxeter element by a quasi-Coxeter element.

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