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Dynamique sur les espaces de représentations de surfaces non-orientables

Abstract : We consider the space of representations Hom(Pi,G) of a surface group Pi into a Lie group G, and the moduli space X(Pi,G) of G-conjugacy classes of such representations. These spaces admit a natural action of the mapping class group of the underlying surface S, and this actions displays very rich dynamics depending on the choice of the Lie group G, and on the connected component of the space that we consider. In this thesis, we focus on the case when S is a non-orientable surface. In the rst part, we study the dynamical properties of the mapping class group actions on the moduli space X(Pi,SU(2)) and prove that this action is ergodic when the Euler characteristic of the surface is less than -1 with respect to a natural measure on the space. In the second part, we show that the representation space Hom (Pi , PSL(2,R)) has two connected components indexed by a Stiefel-Whitney class.
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Contributor : Frederic Palesi <>
Submitted on : Tuesday, January 5, 2010 - 10:31:49 AM
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Frédéric Palesi. Dynamique sur les espaces de représentations de surfaces non-orientables. Mathématiques [math]. Université Joseph-Fourier - Grenoble I, 2009. Français. ⟨tel-00443930⟩

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