Connectivity of complexes of separating curves
Summary: 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.
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