The Goldman symplectic form on the PGL(V)-Hitchin component

Zhe Sun; Tengren Zhang

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arXiv · 1709.03589

The Goldman symplectic form on the PGL(V)-Hitchin component

Zhe Sun·Tengren Zhang

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Abstract

This article is the second of a pair of articles about the Goldman symplectic form on the PGL(V)-Hitchin component of a closed, connected, oriented, hyperbolic surface S. We show that any ideal triangulation on S and any compatible bridge system determine a symplectic trivialization of the tangent bundle to the PGL(V)-Hitchin component of S. Using this, we prove that a large class of vector fields defined in the companion paper [SWZ20] are Hamiltonian. This is then used to prove that the explicit global coordinate system defined in the companion paper [SWZ20] is a global Darboux coordinate system for the PGL(V)-Hitchin component.

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Zhe Sun, Tengren Zhang. 2017-09-11. The Goldman symplectic form on the PGL(V)-Hitchin component. https://arxiv.org/abs/1709.03589

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