|DATE||March 04 (Mon), 2019|
|TITLE||[GS_M_Topo] Symplectic coordinates on 3-Hitchin components|
Goldman parametrizes the 3-Hitchin component of a closed oriented hyperbolic surface of genus g by 16g?16 parameters. Among them, 10g?10 coordinates are canonical. In this paper, we prove that the 3-Hitchin component equipped with the Goldman symplectic form admits a global Darboux coordinate system such that the half of its coordinates are canonical Goldman coordinates. To this end, we prove a version of action-angle principle and a Zocca type decomposition formula for the symplectic form of H. Kim and Guruprasad-Huebschmann-Jeffrey-Weinstein given to each symplectic leaf of the Hitchin component of a compact surface.