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Article Dans Une Revue Annales de l'Institut Fourier Année : 2012

On the ideal triangulation graph of a punctured surface

Résumé

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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Dates et versions

hal-00423547 , version 1 (12-10-2009)

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Mustafa Korkmaz, Athanase Papadopoulos. On the ideal triangulation graph of a punctured surface. Annales de l'Institut Fourier, 2012, 62 (4), p. 1367-1382. ⟨10.5802/aif.2725⟩. ⟨hal-00423547⟩
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