eprintid: 34521
rev_number: 16
eprint_status: archive
userid: 7987
dir: disk0/00/03/45/21
datestamp: 2024-03-13 14:12:13
lastmod: 2024-07-17 11:51:09
status_changed: 2024-03-13 14:12:13
type: doctoralThesis
metadata_visibility: show
creators_name: Magnani, Marta
title: On arc coordinates for maximal representations
subjects: ddc-510
divisions: i-110300
divisions: i-110400
adv_faculty: af-11
abstract: Given a hyperbolic surface with boundary, arc coordinates provide a parametrization of the Teichmüller space. They rely on the choice of a family of arcs which start and end at boundary components and are orthogonal to them. Higher rank Teichmüller theories are a generalization of classical Teichmüller theory and are concerned with the study of representations of the fundamental group of an oriented surface of negative Euler characteristic into simple real Lie groups G of higher rank. It is well known that maximal representations are a higher rank Teichmüller theory for G Hermitian. In this thesis we will discuss how to generalize arc coordinates for maximal representations, focusing on the case where the surface is a pair of pants and G is PSp(4,R). This will be possible by introducing geometric parameters on the space of right-angled hexagons in the Siegel space X, which lead to the visualization of a right-angled hexagon as a polygonal chain inside the hypervolic plane. We discuss geometric properties of reflections in X and introduce the notion of maximal representations of a reflection group W3. We give a parametrization of maximal representations of W3 into PSp(4,R), which allows us to parametrize a subset of maximal and Shilov hyperbolic representations into PSp(4,R).
date: 2024
id_scheme: DOI
id_number: 10.11588/heidok.00034521
ppn_swb: 1883498422
own_urn: urn:nbn:de:bsz:16-heidok-345215
date_accepted: 2024-03-01
advisor: HASH(0x55fc36bd00d8)
language: eng
bibsort: MAGNANIMARONARCCOORD
full_text_status: public
place_of_pub: Heidelberg
citation:   Magnani, Marta  (2024) On arc coordinates for maximal representations.  [Dissertation]     
document_url: https://archiv.ub.uni-heidelberg.de/volltextserver/34521/1/On%20arc%20coordinates%20for%20maximal%20representations.pdf