Curve graphs for Artin–Tits groups of type B , A∼ and C∼ are hyperbolic

Abstract

The graph of irreducible parabolic subgroups is a combinatorial object associated to an Artin–Tits group A defined so as to coincide with the curve graph of the (n+1) ‐times punctured disk when A is Artin's braid group on (n+1) strands. In this case, it is a hyperbolic graph, by the celebrated Masur–Minsky's theorem. Hyperbolicity of the graph of irreducible parabolic subgroups for more general Artin–Tits groups is an important open question. In this paper, we give a partial affirmative answer.