DC Field | Value | Language |
---|---|---|
dc.contributor.advisor | Suh, Dong-Youp | - |
dc.contributor.advisor | 서동엽 | - |
dc.contributor.author | Cho, Yun-Hyung | - |
dc.contributor.author | 조윤형 | - |
dc.date.accessioned | 2011-12-14T04:40:59Z | - |
dc.date.available | 2011-12-14T04:40:59Z | - |
dc.date.issued | 2010 | - |
dc.identifier.uri | http://library.kaist.ac.kr/search/detail/view.do?bibCtrlNo=455387&flag=dissertation | - |
dc.identifier.uri | http://hdl.handle.net/10203/41948 | - |
dc.description | 학위논문(박사) - 한국과학기술원 : 수리과학과, 2010.08, [ iv, 53 p. ] | - |
dc.description.abstract | 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. | eng |
dc.language | eng | - |
dc.publisher | 한국과학기술원 | - |
dc.subject | action | - |
dc.subject | reduction | - |
dc.subject | moment map | - |
dc.subject | symplectic | - |
dc.subject | Hamiltonian | - |
dc.subject | 해밀턴 | - |
dc.subject | 작용 | - |
dc.subject | 축소공간 | - |
dc.subject | 모멘트 | - |
dc.subject | 사교기하 | - |
dc.title | Circle actions on symplectic manifolds | - |
dc.title.alternative | 사교다양체상의 원의 작용에 대한 연구 | - |
dc.type | Thesis(Ph.D) | - |
dc.identifier.CNRN | 455387/325007 | - |
dc.description.department | 한국과학기술원 : 수리과학과, | - |
dc.identifier.uid | 020047584 | - |
dc.contributor.localauthor | Suh, Dong-Youp | - |
dc.contributor.localauthor | 서동엽 | - |
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