Seminar of Algebra

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An analogue of the curve complex for Garside groups

Bert Wiest (University of Rennes 1, France)
Departamento de Álgebra
Thu, 2 jun 2016 12:30
Bert Wiest works at the University of Rennes 1 (France). His research interests are in geometric group theory, particularly in mapping class groups and Garside groups.

Garside groups are a family of groups with particularly nice algorithmic properties, containing in particular all Artin groups of spherical type; the most famous examples are the braid groups. In this talk I will present a simple construction which associates to every Garside group a locally infinite, delta-hyperbolic graph on which the group acts; we call it the "additional length complex" of the group. I will show that these complexes share important features with the curve complexes -- in fact, the additional length complex of the braid group $B_n$ is conjectured to be quasi-isometric to the curve complex of the $n$-times punctured disk. Our construction has the potential to be adapted to many other contexts. (Joint with Matthieu Calvez)