Connectivity of complexes of separating curves
Geometric Topology
2012-02-09 v3 Algebraic Geometry
Abstract
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.
Cite
@article{arxiv.1001.0823,
title = {Connectivity of complexes of separating curves},
author = {Eduard Looijenga},
journal= {arXiv preprint arXiv:1001.0823},
year = {2012}
}
Comments
8 p. This version to be published in Groups, Geometry and Dynamics