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.
SEEK ID: https://publications.h-its.org/publications/1221
DOI: 10.1007/s00039-020-00534-4
Research Groups: Groups and Geometry
Publication type: Journal
Journal: Geometric and Functional Analysis
Citation: Geom. Funct. Anal. 30(2):588-692
Date Published: 1st Apr 2020
Registered Mode: by DOI
Views: 5446
Created: 22nd Feb 2021 at 14:41
Last updated: 5th Mar 2024 at 21:24
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