eprintid: 32000
rev_number: 13
eprint_status: archive
userid: 6843
dir: disk0/00/03/20/00
datestamp: 2022-08-08 10:40:56
lastmod: 2022-08-23 12:21:19
status_changed: 2022-08-08 10:40:56
type: doctoralThesis
metadata_visibility: show
creators_name: Maret, Arnaud
title: The symplectic geometry of surface group representations in genus zero
subjects: ddc-500
subjects: ddc-510
divisions: i-110400
adv_faculty: af-11
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
id_scheme: DOI
id_number: 10.11588/heidok.00032000
ppn_swb: 1815007826
own_urn: urn:nbn:de:bsz:16-heidok-320009
date_accepted: 2022-07-22
advisor: HASH(0x55fc36db99d8)
language: eng
bibsort: MARETARNAUTHESYMPLEC20220725
full_text_status: public
place_of_pub: Heidelberg
citation:   Maret, Arnaud  (2022) The symplectic geometry of surface group representations in genus zero.  [Dissertation]     
document_url: https://archiv.ub.uni-heidelberg.de/volltextserver/32000/1/thesis-administration-version.pdf