The curve complex and its analogues
The curve complex associated to a finite type surface is a simplicial complex which was introduced in the late 70s by Harvey, and has since proved to be a key tool in the study of Teichmuller spaces and mapping class groups. The hyperbolicity of this complex, as proved by Masur and Minsky, was also an important inspiration for the wider study of acylindrically hyperbolic and hierarchically hyperbolic groups.
More recently, several analogues of the curve complex have been introduced for other types of groups and manifolds. Examples include the extension graph for right-angled Artin groups, the contact graph for graph products, the sphere complex for three manifolds, the disc complex for handlebodies, and the fine curve graph for infinite type surfaces. Many of these graphs and complexes have already been shown to have various parallel properties to the curve complex, but none have been explored to the same extent.
The goal of this workshop is to allow early-career researchers to discover and study these analogues of the curve complex, and to work together on open questions in the area.
The workshop is funded by the European Mathematical Society and the projects PLAGE (PLongements, Actions de Groupes, Ergodicité) and GOFr (Groupes Opérant sur des Fractales) of the ANR (Agence Nationale de la Recherche).
