Flows on the PGL(V)-Hitchin component

• Verfasst von: Sun, Zhe [VerfasserIn]
• Verfasst von: Wienhard, Anna [VerfasserIn]
• Verfasst von: Zhang, Tengren [VerfasserIn]
• Titel: Flows on the PGL(V)-Hitchin component
• Verf.angabe: Zhe Sun, Anna Wienhard & Tengren Zhang
• E-Jahr: 2020
• Jahr: 14 May 2020
• Umfang: 5 S.
• Fussnoten: Gesehen am 01.09.2020
• Titel Quelle: Enthalten in: Geometric and functional analysis
• Ort Quelle: Cham (ZG) : Springer International Publishing AG, 1991
• Jahr Quelle: 2020
• Band/Heft Quelle: 30(2020), 2, Seite 588-692
• ISSN Quelle: 1420-8970
• DOI: doi:10.1007/s00039-020-00534-4
• Datenträger: Online-Ressource
• Sprache: eng
• K10plus-PPN: 172851584X

Abstract

In this article we define new flows on the Hitchin components for $$\mathrm {PGL}(V)$$PGL(V). 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 $$n=2$$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 $$\mathrm{PGL} ({V})$$PGL(V)-Hitchin component, 2017. arXiv:1709.03589), this gives a global Darboux coordinate system on the Hitchin component.