Connectivity of complexes of separating curves

Abstract

We prove that the separating curve complex of a closed orientable surface of genus $g$ is $(g-3)$-connected. We also obtain a connectivity property for a separating curve complex of the open surface that is obtained by removing a finite set from a closed one, where it is assumed that the removed set is endowed with a partition and that the separating curves respect that partition. These connectivity statements have implications for the algebraic topology of the moduli space of curves.