一個在T*RP2上的單調拉格朗日環面

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陳浚廷(Jyun-Ting Chen) 查詢紙本館藏

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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)

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摘要(中)

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。

摘要(英)

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.

關鍵字(中)

★ 拉格朗日環面
★ 不可置換
★ 單調

關鍵字(英)

★ non-displaceable
★ monotone
★ Lagrangian torus

論文目次

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

參考文獻

[1] Albers, P. and Frauenfelder, U.,A Nondisplaceable Lagrangian Torus in
T S2. Comm. Pure Appl. Math., 1046-1051, 2008.
[2] Ana Cannas da Silva, Lectures on Symplectic Geometry . Springer-Verlag,
2008.
[3] Banyaga, A. and Hurtubise, D. Lectures On Morse Homology. Springer-
Verlag, 2010.
[4] Biran, P. and Cornea, O. Rigidity and uniruling for Lagrangian subman-
ifolds. Geom. Topol., 2881-2989, 13(2009).
[5] Byun, Y. Maslov indices in practice. Info. Center for Math. Sci., 2002.
[6] Floer, A., Morse theory for Lagrangian intersections. J. Di erential Geometry,
513-547, 28(1988).
[7] Floer, A., A relative Morse index for the symplectic action. Comm. Pure
Appl. Math., 393-407, 41(1988).
[8] Floer, A., The unregularized gradient
ow of the symplectic action.
Comm. Pure Appl. Math., 775-813, 41(1988).
[9] Khovanov, M. and Seidel, P., Quivers, Floer cohomology, and braid group
actions. J. Amer. Math. Soc. 15,No. 1, 203-271,2002.
[10] Lee, J., Riemannian Manifolds, Springer-Verlag, 1997.
[11] McDu , D. and Salamon, D.,Introduction to Symplectic Topology. Oxford
University Press,1998.
[12] Milnor, J. and Stashe , J.,Characteristic Classes. Princeton University
Press, 1974.
[13] Oh, Y. G., Floer cohomology of Lagrangian intersections and pseudo-
holomorphisc disks I. Comm. Pure Appl. Math., 949-994, 1993.
[14] Oh, Y. G., Addendum to " Floer Cohomology of Lagrangian Intersec-
tions and Pseudo-Holomorphic Discs, I". Comm. Pure Appl. Math., 1299-
1302, 1995.
[15] Pozniak, M. Floer homology, Novikov rings and clean intersections.
Northern California Symplectic Geometry Seminar, 119-181. AMS Translations
Series 2, 196,1999.
[16] Viterbo, C. Intersection de sous-varietes lagrangiennes, fonctionnelles
d’’action et indice des systemes hamiltoniens. Bulletin de la S. M. F.,
1987.

指導教授

姚美琳(Mei-Lin Yau)

審核日期

2012-7-24

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