Groups, Geometry, and Dynamics
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Published online: 2013-05-07
Connectivity of complexes of separating curvesEduard Looijenga (1) Tsinghua University, Beijing, Haidan District, China
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.
Keywords: Separating curve complex
Looijenga Eduard: Connectivity of complexes of separating curves. Groups Geom. Dyn. 7 (2013), 443-450. doi: 10.4171/GGD/189