On the ideal triangulation graph of a punctured surface (original) (raw)
2012, Annales de l’institut Fourier
We study the ideal triangulation graph T (S) of a punctured surface S of finite type. We show that if S is not the sphere with at most three punctures or the torus with one puncture, then the natural map from the extended mapping class group of S into the simplicial automorphism group of T (S) is an isomorphism. We also show that under the same conditions on S, the graph T (S) equipped with its natural simplicial metric is not Gromov hyperbolic. Thus, from the point of view of Gromov hyperbolicity, the situation of T (S) is different from that of the curve complex of S.
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