On the ideal triangulation graph of a punctured surface

الأصل · EN

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.