Asymptotic dimension of planes

Contact: Elia Fioravanti (fioravanti@mpim-bonn.mpg.de)

Asymptotic dimension was introduced by Gromov as dimension of a metric space that is invariant by quasi-isometry. We prove that a plane with any geodesic metric has asymptotic dimension at most three. In the proof, a cactus plays an important role. A cactus is a connected graph in which any two simple cycles have at most one vertex in common. We give a characterization of a graph that is quasi-isometric to a cactus. This is a joint work with Papasoglu.