Circle actions on symplectic manifolds = 사교다양체상의 원의 작용에 대한 연구

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This thesis consists of two parts. The first part is as follows. Let ($\It{M, w}$) be a 6-dimensional closed symplectic semifree $\It{S}^1$-manifold whose fixed point set is a disjoint union of surfaces. Suppose that there is a generalized moment map. We prove that the action is Hamiltonian if and only if $\It{M_red}$ is diffeomorphic to an $\It{S}^2$-bundle over some compact Riemann surface and the fixed point set is not empty. We also show that the number of fixed surfaces of genus > 0 is at most four if the action is Hamiltonian. Moreover, if the minimum and the maximum are 2-spheres, then there is at most one fixed surface of non-zero genus. The second part is about the log-concavity properties on symplectic manifolds. we define a notion “(Strong)Log-concavity property” on symplectic manifolds and prove that for a given symplectic manifold $\It{M}$ satisfying the strong log-concavity property, the symplectic blow-ups and blow-downs along symplectic submanifolds of a small $\epsilon$-amount satisfy the log-concavity property. Moreover, we explain that these properties are closely related to the moduli space of symplectic structures.
Advisors
Suh, Dong-Youpresearcher서동엽researcher
Description
한국과학기술원 : 수리과학과,
Publisher
한국과학기술원
Issue Date
2010
Identifier
455387/325007  / 020047584
Language
eng
Description

학위논문(박사) - 한국과학기술원 : 수리과학과, 2010.08, [ iv, 53 p. ]

Keywords

action; reduction; moment map; symplectic; Hamiltonian; 해밀턴; 작용; 축소공간; 모멘트; 사교기하

URI
http://hdl.handle.net/10203/41948
Link
http://library.kaist.ac.kr/search/detail/view.do?bibCtrlNo=455387&flag=dissertation
Appears in Collection
MA-Theses_Ph.D.(박사논문)
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