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Real Lagrangians in symplectic toric manifolds
| DC Field | Value | Language |
|---|---|---|
| dc.contributor.advisor | 최수영 | - |
| dc.contributor.author | 문지연 | - |
| dc.date.accessioned | 2022-11-29T02:32:46Z | - |
| dc.date.available | 2022-11-29T02:32:46Z | - |
| dc.date.issued | 2021-08 | - |
| dc.identifier.other | 31222 | - |
| dc.identifier.uri | https://dspace.ajou.ac.kr/handle/2018.oak/20355 | - |
| dc.description | 학위논문(박사)--아주대학교 일반대학원 :수학과,2021. 8 | - |
| dc.description.tableofcontents | chapter 1. Introduction 1 section 1.1 On the topology of real Lagrangians 2 section 1.2 On the space of antisymplectic involutions 6 chapter 2. Preliminaries 9 section 2.1 Symplectic manifold ans its Lagrangian submanifolds 9 section 2.2 Hamiltonian vector fields and Hamiltonian torus actions 13 section 2.3 Properties of Hamiltonian T-space 16 section 2.4 Morphisms compatible with a Hamiltonian torus action 21 section 2.5 Symplectic toric maniflds 24 chapter 3. Delzant construction 27 section 3.1 Proof of Delzant theorem 28 chapter 4. Lifted antisymplectic involutions from moment polytopes 35 section 4.1 Symmetries of polygons 35 section 4.2 Lifting of symmetries 36 chapter 5. Real Delzant construction 41 section 5.1 Real Delzant construction 41 chapter 6. Applications of real Delzant construction 51 section 6.1 Convexity and tightness 51 section 6.2 Real Lagrangians in toric symplectic del Pezzo surfaces 55 chapter 7. Antisymplectic involutions of $S^2\times S^2$ 69 section 7.1 J-holomorphic curves and Moduli spaces 72 section 7.2 Gromov's foliations on $S^2\timesS^2$ 76 section 7.3 Real analogue of the work of Hind 78 section 7.4 Diffeomorphism of Q induced by transversal foliations 81 section 7.5 Equivariant Moser trick 83 | - |
| dc.language.iso | eng | - |
| dc.publisher | The Graduate School, Ajou University | - |
| dc.rights | 아주대학교 논문은 저작권에 의해 보호받습니다. | - |
| dc.title | Real Lagrangians in symplectic toric manifolds | - |
| dc.type | Thesis | - |
| dc.contributor.affiliation | 아주대학교 일반대학원 | - |
| dc.contributor.department | 일반대학원 수학과 | - |
| dc.date.awarded | 2021. 8 | - |
| dc.description.degree | Doctoral | - |
| dc.identifier.localId | 1227092 | - |
| dc.identifier.uci | I804:41038-000000031222 | - |
| dc.identifier.url | https://dcoll.ajou.ac.kr/dcollection/common/orgView/000000031222 | - |
| dc.subject.keyword | Delzant construction | - |
| dc.subject.keyword | Gromov foliation | - |
| dc.subject.keyword | antisymplectic involution | - |
| dc.subject.keyword | real Lagrangian | - |
| dc.subject.keyword | toric symplectic manifold | - |
| dc.description.alternativeAbstract | We study two problems of real aspects in symplectic topology. The first problem concerns the topology of real Lagrangian submanifolds in a toric symplectic manifold. Real Lagrangians we consider come from involutive symmetries on the moment polytope of a toric symplectic manifold. We establish a real analogue of the Delzant construction for those real Lagrangians, which says that their diffeomorphism type is determined by combinatorial data of the polytope. As an application, we realize all possible diffeomorphism types of connected real Lagrangians in toric symplectic del Pezzo surfaces. In the second problem, we deal with a real analogue of the symplectic mapping class group of a monotone $Q:=S^2\times S^2$, the set $\pi_{0}\mathcal{I}(Q,\ow ,S^2)$ of the isotopy classes of antisymplectic involutions of $Q$ having a Lagrangian sphere as the fixed point set. It is shown that $\pi_{0}\mathcal{I}(Q,\ow ,S^2)$ has a single element. This follows from a stronger result, namely that any two anti-symplectic involutions in that space are Hamiltonian isotopic. | - |
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- Graduate School of Ajou University > Department of Mathematics > 4. Theses(Ph.D)
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