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primary topic: The symplectic geometry of surface group representations in genus zero

The symplectic geometry of surface group representations in genus zero
type: Article
abstract: 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
author list: authors
type: EPrint
type: DoctoralThesisEPrint
is part of: repository
has document: The symplectic geometry of surface group representations in genus zero (PDF)
has document: The symplectic geometry of surface group representations in genus zero (Other)
subject: 500 Naturwissenschaften und Mathematik
subject: 510 Mathematik

The symplectic geometry of surface group representations in genus zero (PDF)
type: Document
has file: thesis-administration-version.pdf
has part: thesis-administration-version.pdf

Arnaud Maret
type: Person
given name: Arnaud
family name: Maret

The symplectic geometry of surface group representations in genus zero (Other)
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The symplectic geometry of surface group representations in genus zero (Other)
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The symplectic geometry of surface group representations in genus zero (Other)
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The symplectic geometry of surface group representations in genus zero (Other)
type: Document
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The symplectic geometry of surface group representations in genus zero (Other)
type: Document
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HTML Summary of #32000 The symplectic geometry of surface group representations in genus zero
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primary topic: The symplectic geometry of surface group representations in genus zero

500 Naturwissenschaften und Mathematik
type: Concept
preferred label: 500 Natural sciences and mathematics @en

510 Mathematik
type: Concept
preferred label: 510 Mathematics @en