Symplectic coordinates on PSL3(R)-Hitchin components

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Goldman parametrizes the PSL 3 (R) -Hitchin component of a closed oriented hyperbolic surface of genus g by 16g−16 parameters. Among them, 10g−10 coordinates are canonical. We prove that the PSL 3 (R)-Hitchin component equipped with the Atiyah–Bott–Goldman symplectic form admits a global Darboux coordinate system such that the half of its coordinates are canonical Goldman coordinates. To this end, we show a version of the action-angle principle and the Zocca-type decomposition formula for the symplectic form of H. Kim and Guruprasad–Huebschmann–Jeffrey-Weinstein given to symplectic leaves of the Hitchin component.
Publisher
INT PRESS BOSTON
Issue Date
2020-12
Language
English
Article Type
Article
Citation

PURE AND APPLIED MATHEMATICS QUARTERLY, v.16, no.5, pp.1321 - 1386

ISSN
1558-8599
DOI
10.4310/PAMQ.2020.v16.n5.a1
URI
http://hdl.handle.net/10203/280727
Appears in Collection
MA-Journal Papers(저널논문)
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