bertold.wiest@univ-rennes1.fr
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)