Fragmentation et propriétés algébriques des groupes d'homéomorphismes

Abstract : In this thesis, we are interested in various algebraic properties of groups of homeomorphisms and diffeomorphisms of manifolds. We call fragmentation the possibility to write a homeomorphism as a composition of homeomorphisms supported in balls. First, we study the commutator length on the group of homeomorphisms of the torus and of the annulus, as well as the fragmentation norm, which associates to any homeomorphism the minimal number of factors necessary to write this homeomorphism as a composition of homeomorphisms supported in balls. In a second part of this thesis, we deal with another algebraic property of homeomorphism and diffeomorphism groups: the distortion. This last notion is surprisingly related to fragmentation properties of homeomorphisms.
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Emmanuel Militon. Fragmentation et propriétés algébriques des groupes d'homéomorphismes. Mathématiques générales [math.GM]. Université Paris Sud - Paris XI, 2012. Français. ⟨NNT : 2012PA112246⟩. ⟨tel-00752638⟩

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