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研究生： 陳浚廷
Jyun-Ting Chen
論文名稱： 一個在T*RP2上的單調拉格朗日環面
A monotone Lagrangian torus in T*RP2
指導教授： 姚美琳
Mei-Lin Yau
口試委員:
學位類別： 碩士
Master
系所名稱： 理學院 - 數學系
Department of Mathematics
畢業學年度： 100
語文別： 英文
論文頁數： 35
中文關鍵詞： 拉格朗日環面 、不可置換 、單調
外文關鍵詞： non-displaceable, monotone, Lagrangian torus
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    • Poterovich在T^* S^2上構造了一個單調拉格朗日環面，Albers和Frauenfelder接著證明了這個環面是不可置換的(non-displaceable)。我們利用類似的構造方式在T^* RP^2上造了一個單調拉格朗日環面，並提出一些觀察，試著解釋這個環面是不可置換的可能性。

    Leonid Poterovich constructed a Lagrangian torus in T^* S^2 and then Albers and Frauenfelder proved that Lagrangian torus is non-displaceable. We use similar construction to construct a monotone Lagrangian torus in T^* RP^2. Moreover, we provide some observations explaining this monotone Lagrangian torus would be non-displaceable.

    摘要 i Abstract ii Contents iii 1 Introduction 1 2 Notation and definition 2 2.1 Symplectic manifolds and symplectomorphism 2 2.2 Cotangent bundle with canonical form 3 2.3 Almost complex structure 3 2.4 Chern classes and monotonicity 4 2.5 Symplectic and Hamiltonian vector fields 5 2.6 Lagrangian submanifolds 6 2.7 Maslov index 8 2.7.1 Maslov index for L_n 8 2.7.2 Maslov index for π_2 (M,L) 9 2.7.3 Maslov-Viterbo index 10 2.8 Floer homology 10 2.8.1 Lagrangian intersection Floer cohomology 11 2.8.2 Lagrangian intersection Floer homology 13 3 Non-displaceable Lagrangian torus in T^* S^2 13 3.1 Construction of monotone Lagrangian torus 13 3.2 Non-displaceability 16 4 A monotone Lagrangian torus in T^* RP^2 21 5 Discussion 25 References 27

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