<> "The repository administrator has not yet configured an RDF license."^^ . <> . . "Geometric structures and representations of\r\nsurface groups"^^ . "Representations of hyperbolic groups into higher rank Lie groups has been an\r\nactive topic of study in recent years. In particular the character variety associ-\r\nated with a surface group for some semi-simple Lie group of non-compact type\r\nadmits remarkable connected components containing only discrete and faithful\r\nrepresentations. A union of such connected components is called a higher rank\r\nTeichmüller space. In all the known cases, the representations in these compo-\r\nnents all satisfy an Anosov property, which is a dynamical property stronger\r\nthan being discrete and faithful. Some of these spaces can be interpreted as\r\nspaces of geometric structures: as for instance convex projective structures on\r\nsurfaces, or fibered photon structures.\r\nIn this thesis, we bring original contributions to this area, focusing in par-\r\nticular on the locally symmetric space and parabolic structures associated to\r\nAnosov representations. The first part of this thesis is rather general, and dis-\r\ncuss parabolic structures constructed using a domain of discontinuity as well\r\nas their relation with the locally symmetric space for certain Anosov repre-\r\nsentations. We study more precisely the domains of discontinuity that can be\r\ninterpreted as domains of proper Busemann functions.\r\nThe second part focuses on maximal representations in Spp2n, Rq, a particu-\r\nlar class of higher rank Teichmüller spaces. We characterize maximal represen-\r\ntations in terms of geometric structures that admit a special fibration. Finally\r\nwe study maximal representations that are also Borel Anosov, and show in par-\r\nticular that in Spp4, Rq these representations are Hitchin, answering a question\r\nfrom Canary.\r\nThis thesis encompasses the results of the arxiv preprints Nearly geodesic\r\nimmersions and domains of discontinuity [Dav23] and Finite-sided Dirichlet\r\ndomains for Anosov subgroups [DR24] , a future preprint Geometric structures\r\nfor maximal representations and pencils , and finally the article Maximal and\r\nBorel Anosov representations in Spp2n, Rq [Dav24]. The preprint [DR24] is joint\r\nwork with Max Riestenberg"^^ . "2024" . . . . . . . "Colin"^^ . "Davalo"^^ . "Colin Davalo"^^ . . . . . . "Geometric structures and representations of\r\nsurface groups (PDF)"^^ . . . "Thesis DAVALO final.pdf"^^ . . . "Geometric structures and representations of\r\nsurface groups (Other)"^^ . . . . . . "indexcodes.txt"^^ . . . "Geometric structures and representations of\r\nsurface groups (Other)"^^ . . . . . . "lightbox.jpg"^^ . . . "Geometric structures and representations of\r\nsurface groups (Other)"^^ . . . . . . "preview.jpg"^^ . . . "Geometric structures and representations of\r\nsurface groups (Other)"^^ . . . . . . "medium.jpg"^^ . . . "Geometric structures and representations of\r\nsurface groups (Other)"^^ . . . . . . "small.jpg"^^ . . "HTML Summary of #35082 \n\nGeometric structures and representations of \nsurface groups\n\n" . "text/html" . . . "510 Mathematik"@de . "510 Mathematics"@en . .