Flows on the $$\mathbf{PGL(V)}$$-Hitchin Component

Abstract:

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

Authors: Zhe Sun, Anna Wienhard, Tengren Zhang

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Citation
Sun, Z., Wienhard, A., & Zhang, T. (2020). Flows on the $$\mathbf{PGL(V)}$$-Hitchin Component. In Geometric and Functional Analysis (Vol. 30, Issue 2, pp. 588–692). Springer Science and Business Media LLC. https://doi.org/10.1007/s00039-020-00534-4
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Created: 22nd Feb 2021 at 14:41

Last updated: 5th Mar 2024 at 21:24

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