Article (Scientific journals)
Flows on the PSL(V)-Hitchin component
Sun, Zhe; Wienhard, Anna; Zhang, Tengren
2020In Geometric and Functional Analysis, 30, p. 588–692
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Keywords :
Hitchin components; Flows; Global coordinate system
Abstract :
[en] In this article we define new flows on the Hitchin components for PSL(n,R). Special examples of these flows are associated to simple closed curves on the surface and give generalized twist flows. Other examples, so called eruption flows, are associated to pair of pants in S and capture new phenomena which are not present in the case when n = 2. We determine a global coordinate system on the Hitchin component. Using the computation of the Goldman symplectic form on the Hitchin component, that is developed by two of the authors in a companion paper to this article (Sun and Zhang in The Goldman symplectic form on the PGL(V)-Hitchin component, 2017. arXiv:1709.03589), this gives a global Darboux coordinate system on the Hitchin component.
Disciplines :
Mathematics
Author, co-author :
Sun, Zhe ;  University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit
Wienhard, Anna;  Universität Heidelberg > Mathematisches Institut
Zhang, Tengren;  National University of Singapore > Department of Mathematics
External co-authors :
yes
Language :
English
Title :
Flows on the PSL(V)-Hitchin component
Publication date :
2020
Journal title :
Geometric and Functional Analysis
ISSN :
1420-8970
Publisher :
Birkhauser Verlag, Switzerland
Volume :
30
Pages :
588–692
Peer reviewed :
Peer Reviewed verified by ORBi
European Projects :
FP7 - 614733 - GEOMETRICSTRUCTURES - Deformation Spaces of Geometric Structures
FnR Project :
FNR13242285 - COmbinatorial and ALgebraic Aspects of Surface group representations, 2017 (01/09/2018-31/08/2020) - Zhe Sun
Funders :
CE - Commission Européenne [BE]
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