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Topologie et géométrie des complexes de groupes à courbure négative ou nulle

Abstract : Given a complex of groups, when is it possible to deduce a property for its fundamental group out of the analogous properties of its local groups? This natural problem of geometric group theory has been adressed mainly for graphs of groups and complexes of finite groups. In this thesis, we develop geometric tools to study non-positively curved complexes of groups. We focus on properties of an asymptotic nature: EZ-structures, hyperbolicity. This allows us to prove a combination theorem for hyperbolic groups, which generalises a theorem of Bestvina-Feighn to complexes of groups of arbitrary dimension.
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Alexandre Martin. Topologie et géométrie des complexes de groupes à courbure négative ou nulle. Mathématiques générales [math.GM]. Université de Strasbourg, 2013. Français. ⟨NNT : 2013STRAD005⟩. ⟨tel-00821442v3⟩

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