Connectivity of complexes of separating curves

Details Connectivity of complexes of separating curves Connectivity of complexes of separating curves

2010-01-06

arxiv.org/abs/1001.0823v3

Mathematics

Geometric Topology

8 p. This version to be published in Groups, Geometry and Dynamics

Scientific paper

We prove that the separated curve complex of a closed orientable surface of genus g is (g-3)-connected. We also obtain a connectivity property for a separated curve complex of the open surface that is obtained by removing a finite set from a closed one, but it is then 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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