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See detailFlows on the PSL(V)-Hitchin component
Sun, Zhe UL; Wienhard, Anna; Zhang, Tengren

in Geometric and Functional Analysis (2020), 30

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 ... [more ▼]

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. [less ▲]

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See detailThe Goldman symplectic form on the PSL(V)-Hitchin component
Sun, Zhe UL; Zhang, Tengren

E-print/Working paper (2017)

This article is the second of a pair of articles about the Goldman symplectic form on the PSL(V )-Hitchin component. We show that any ideal triangulation on a closed connected surface of genus at least 2 ... [more ▼]

This article is the second of a pair of articles about the Goldman symplectic form on the PSL(V )-Hitchin component. We show that any ideal triangulation on a closed connected surface of genus at least 2, and any compatible bridge system determine a symplectic trivialization of the tangent bundle to the Hitchin component. Using this, we prove that a large class of flows defined in the companion paper [SWZ17] are Hamiltonian. We also construct an explicit collection of Hamiltonian vector fields on the Hitchin component that give a symplectic basis at every point. These are used in the companion paper to compute explicit global Darboux coordinates for the Hitchin component. [less ▲]

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