On the arc and curve complex of a surface
Résumé
We study the {\it arc and curve} complex $AC(S)$ of an oriented connected surface $S$ of finite type with punctures. We show that except for some finitely many special surfaces, the simplicial automorphism group of $AC(S)$ coincides with the natural image of the extended mapping class group of $S$ in that group. We also show that for any vertex of $AC(S)$, the combinatorial structure of the link of that vertex is sufficient to characterize the topological type of the curve or of the arc on $S$ that represents this vertex. Finally, we show that the natural embedding of the curve complex in $AC(S)$ is a quasi-isometry.
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