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We study the ideal triangulation graph of an oriented punctured surface of finite type. We show that if 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 into the simplicial automorphism group of is an isomorphism. We also show that the graph of such a surface , equipped with its natural simplicial metric is not Gromov hyperbolic. We also show that if the triangulation graph of two oriented punctured...
It is well known that versal deformations of nonsimple singularities depend on moduli. However they can be topologically trivial along some or all of them. The first step in the investigation of this phenomenon is to determine the versal discriminant (unstable locus), which roughly speaking is the obstacle to analytic triviality. The next one is to construct continuous liftable vector fields smooth far from the versal discriminant and to integrate them. In this paper we extend the results of J....
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