The separating systole on a closed Riemannian surface is defined as the length of the shortest noncontractible loop which is homologically trivial. We answer positively a question of M. Gromov about the asymptotic estimate on the separating systole. Specifically, we show that that the separating systole of a closed Riemannian surface of genus and area g satisfies an upper bound similar to M. Gromov's asymptotic estimate on the homotopy systole.
Geometry-Topology Seminar
Thursday, February 2, 2006 - 4:30pm
Stephane Sabourau
University of Pennsylvania