We prove that the separating curve complex of a closed orientable surface of genus is -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.
Cite this article
Eduard Looijenga, Connectivity of complexes of separating curves. Groups Geom. Dyn. 7 (2013), no. 2, pp. 443–450DOI 10.4171/GGD/189