Compactifications géométriques dans les groupes, les espaces symétriques et les immeubles

Abstract : In our thesis, we focus on various geometric compactifications. We describe the space of closed subgroups of RxZ. We study the Chabauty compactification of symmetric spaces of non-compact type. We define and study the Chabauty compactification of the space of maximal flats of the symmetric spaces of SL3(R) and SL4(R). We study the geometric limits of maximal flats in the symmetric space or in the Bruhat-Tits building associated to SL3 over a local field. We define and study a Thurston-like compactification of spaces of isometry classes of marked lattices. We define a Thurston-like compactification of the Torelli space of a surface and we describe the natural stratification of a subset of the boundary.
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Thomas Haettel. Compactifications géométriques dans les groupes, les espaces symétriques et les immeubles. Mathématiques générales [math.GM]. Université Paris Sud - Paris XI, 2011. Français. ⟨NNT : 2011PA112324⟩. ⟨tel-00662021⟩

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