Geodesic
Connectivity of complexes of separating curves
Eduard Looijenga1
1Tsinghua University, Beijing, Haidan District, China
Groups, geometry, and dynamics, Tome 7 (2013) no. 2, pp. 443-450

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DOI

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.
DOI : 10.4171/ggd/189
Classification : 57-XX, 55-XX, 00-XX
Mots-clés : Separating curve complex

Eduard Looijenga  1

1 Tsinghua University, Beijing, Haidan District, China 
Eduard Looijenga. Connectivity of complexes of separating curves. Groups, geometry, and dynamics, Tome 7 (2013) no. 2, pp. 443-450. doi: 10.4171/ggd/189
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     title = {Connectivity of complexes of separating curves},
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     pages = {443--450},
     year = {2013},
     volume = {7},
     number = {2},
     doi = {10.4171/ggd/189},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/ggd/189/}
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