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On the ideal triangulation graph of a punctured surface

Mustafa Korkmaz, Athanase Papadopoulos (2012)

Annales de l’institut Fourier

We study the ideal triangulation graph T ( S ) of an oriented 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 the graph T ( S ) of such a surface S , equipped with its natural simplicial metric is not Gromov hyperbolic. We also show that if the triangulation graph of two oriented punctured...

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