Symplectic coordinates on $\operatorname{PSL}_3 (\mathbb{R}$)-Hitchin components = $\operatorname{PSL}_3 (\mathbb{R}$)-Hitchin 컴포넌트 위의 사교좌표계

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Goldman parametrizes the $\operatorname{PSL}_3 (\mathbb{R})$-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 $\operatorname{PSL}_3 (\mathbb{R})$-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.
Advisors
Choi, Suhyoungresearcher최서영researcher
Description
한국과학기술원 :수리과학과,
Publisher
한국과학기술원
Issue Date
2019
Identifier
325007
Language
eng
Description

학위논문(박사) - 한국과학기술원 : 수리과학과, 2019.8,[iii, 48 p. :]

Keywords

Global darboux coordinates▼ahitchin component▼agoldman coordinates▼agoldman symplectic form; 글로벌 Darboux 좌표계▼aHitchin 컴포넌트▼aGoldman 좌표계▼aGoldman 사교형식

URI
http://hdl.handle.net/10203/283240
Link
http://library.kaist.ac.kr/search/detail/view.do?bibCtrlNo=871407&flag=dissertation
Appears in Collection
MA-Theses_Ph.D.(박사논문)
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