An analogue of the curve complex for Garside groups

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• Bertold Wiest (Université de Rennes 1)
• Wednesday 16 May 2018, 16:00-17:00
• MR13.

If you have a question about this talk, please contact Oscar Randal-Williams.

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.)

This talk is part of the Differential Geometry and Topology Seminar series.

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