The Goldman symplectic form on the PGL(V)-Hitchin component
Differential Geometry
2023-08-15 v4
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.
Keywords
Cite
@article{arxiv.1709.03589,
title = {The Goldman symplectic form on the PGL(V)-Hitchin component},
author = {Zhe Sun and Tengren Zhang},
journal= {arXiv preprint arXiv:1709.03589},
year = {2023}
}
Comments
79 pages, 17 figures