Reference : The Goldman symplectic form on the PSL(V)-Hitchin component
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The Goldman symplectic form on the PSL(V)-Hitchin component
Sun, Zhe mailto [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >]
Zhang, Tengren mailto [National University of Singapore > Department of Mathematics]
[en] Hitchin component ; Goldman symplectic form ; Hamiltonian vector fields
[en] 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.
FnR ; FNR13242285 > Zhe Sun > > COmbinatorial and ALgebraic Aspects of Surface group representations. > 01/09/2018 > 31/08/2020 > 2017

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