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.
Links:
[1] http://www.mpim-bonn.mpg.de/de/taxonomy/term/39
[2] http://www.mpim-bonn.mpg.de/de/node/4234
[3] http://www.mpim-bonn.mpg.de/de/node/3207