<> "The repository administrator has not yet configured an RDF license."^^ . <> . . "The symplectic geometry of surface group representations in genus zero"^^ . "We study a compact family of totally elliptic representations of the fundamental group of\r\na punctured sphere into PSL(2,R), discovered by Deroin and Tholozan and named after them. We describe a polygonal model that parametrizes the relative character variety of\r\nDeroin–Tholozan representations in terms of chains of triangles in the hyperbolic plane. We extract action-angle coordinates from our polygonal model as geometric quantities\r\nassociated to chains of triangles. The coordinates give an explicit isomorphism between the space of representations and the complex projective space. We prove that they are\r\nalmost global Darboux coordinates for the Goldman symplectic form.\r\n\r\nThis work also investigates the dynamics of the mapping class group action on the rela-\r\ntive character variety of Deroin–Tholozan representations. We apply symplectic methods\r\ndeveloped by Goldman and Xia to prove that the action is ergodic."^^ . "2022" . . . . . . . "Arnaud"^^ . "Maret"^^ . "Arnaud Maret"^^ . . . . . . "The symplectic geometry of surface group representations in genus zero (PDF)"^^ . . . "thesis-administration-version.pdf"^^ . . . "The symplectic geometry of surface group representations in genus zero (Other)"^^ . . . . . . "indexcodes.txt"^^ . . . "The symplectic geometry of surface group representations in genus zero (Other)"^^ . . . . . . "lightbox.jpg"^^ . . . "The symplectic geometry of surface group representations in genus zero (Other)"^^ . . . . . . "preview.jpg"^^ . . . "The symplectic geometry of surface group representations in genus zero (Other)"^^ . . . . . . "medium.jpg"^^ . . . "The symplectic geometry of surface group representations in genus zero (Other)"^^ . . . . . . "small.jpg"^^ . . "HTML Summary of #32000 \n\nThe symplectic geometry of surface group representations in genus zero\n\n" . "text/html" . . . "500 Naturwissenschaften und Mathematik"@de . "500 Natural sciences and mathematics"@en . . . "510 Mathematik"@de . "510 Mathematics"@en . .