Asymptotic bounds for separating systoles on surfaces

  • Stéphane Sabourau

    Université de Tours, France


The separating systole on a closed Riemannian surface M, denoted by sys0(M), is defined as the length of the shortest noncontractible loops which are homologically trivial. We answer positively a question of M. Gromov [Gr96, 2.C.2.(d)] about the asymptotic estimate on the separating systole. Specifically, we show that the separating systole of a closed Riemannian surface M of genus and area g satisfies an upper bound similar to M. Gromov’s asymptotic estimate on the (homotopy) systole. That is, sys0(M) is less than or equivalent to log g.

Cite this article

Stéphane Sabourau, Asymptotic bounds for separating systoles on surfaces. Comment. Math. Helv. 83 (2008), no. 1, pp. 35–54

DOI 10.4171/CMH/117