title: The symplectic geometry of surface group representations in genus zero
creator: Maret, Arnaud
subject: ddc-500
subject: 500 Natural sciences and mathematics
subject: ddc-510
subject: 510 Mathematics
description: We study a compact family of totally elliptic representations of the fundamental group of  a 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  Deroin–Tholozan representations in terms of chains of triangles in the hyperbolic plane. We extract action-angle coordinates from our polygonal model as geometric quantities  associated 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  almost global Darboux coordinates for the Goldman symplectic form.    This work also investigates the dynamics of the mapping class group action on the rela-  tive character variety of Deroin–Tholozan representations. We apply symplectic methods  developed by Goldman and Xia to prove that the action is ergodic.
date: 2022
type: Dissertation
type: info:eu-repo/semantics/doctoralThesis
type: NonPeerReviewed
format: application/pdf
identifier: https://archiv.ub.uni-heidelberg.de/volltextserverhttps://archiv.ub.uni-heidelberg.de/volltextserver/32000/1/thesis-administration-version.pdf
identifier: DOI:10.11588/heidok.00032000
identifier: urn:nbn:de:bsz:16-heidok-320009
identifier:   Maret, Arnaud  (2022) The symplectic geometry of surface group representations in genus zero.  [Dissertation]     
relation: https://archiv.ub.uni-heidelberg.de/volltextserver/32000/
rights: info:eu-repo/semantics/openAccess
rights: http://archiv.ub.uni-heidelberg.de/volltextserver/help/license_urhg.html
language: eng