A study on Hamiltonian circle actions = 해밀토니안 원 작용에 대한 연구

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We present two results on symplectic manifolds with a Hamiltonian circle action. The first one is on the computation of the Gromov width. Let $(M, \omega)$ be a closed monotone symplectic manifold. Suppose there is a semifree Hamiltonian circle action on $(M, \omega)$ with isolated maximum. We prove that the Gromov width of $(M, \omega)$ is given by the difference of the maximum and the second maximum critical values of the moment map. The second one is on the fixed point set of the action. Consider a 6-dimensional closed symplectic manifold with a semifree Hamiltonian circle action. If all fixed components are 2-dimensional, then the number of fixed surfaces of positive genus is 0, 1, 3, or 4.
Suh, Dong-Youpresearcher서동엽
Description
한국과학기술원 : 수리과학과,
Publisher
한국과학기술원
Issue Date
2013
Identifier
565562/325007  / 020057669
Language
eng
Description

학위논문(박사) - 한국과학기술원 : 수리과학과, 2013.8, [ iv, 35 p. ]

Keywords

symplectic manifold; 사이델 표현; 그로모프-위튼 불변량; 그로모프 너비; 해밀토니안 원 작용; 심플렉틱 다양체; Hamiltonian circle action; Gromov width; Gromov-Witten invariant; Seidel representation

URI
http://hdl.handle.net/10203/197740