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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...

On the topological triviality along moduli of deformations of J k , 0 singularities

Piotr Jaworski (2000)

Annales Polonici Mathematici

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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