\`x^2+y_1+z_12^34\`
Advanced Search
Article Contents
Article Contents

Notes on monotone Lagrangian twist tori

Abstract / Introduction Related Papers Cited by
  • We construct monotone Lagrangian tori in the standard symplectic vector space, in the complex projective space and in products of spheres. We explain how to classify these Lagrangian tori up to symplectomorphism and Hamiltonian isotopy, and how to show that they are not displaceable by Hamiltonian isotopies.
    Mathematics Subject Classification: 53D12, 58D10.

    Citation:

    \begin{equation} \\ \end{equation}
  • [1]

    P. Albers and U. Frauenfelder, A non-displaceable Lagrangian torus in $T^$*$S^2$, Comm. Pure Appl. Math., 61 (2008), 1046-1051.doi: doi:10.1002/cpa.20216.

    [2]

    V. I. Arnold, On a characteristic class entering into conditions of quantization, Funkcional. Anal. i Prilozen., 1 (1967), 1-14.doi: doi:10.1007/BF01075861.

    [3]

    D. Auroux, Mirror symmetry and T-duality in the complement of an anticanonical divisor, J. Gökova Geom. Topol., 1 (2007), 51-91.

    [4]

    P. Biran and O. Cornea, A Lagrangian quantum homology, in "New Perspectives and Challenges in Symplectic Field Theory," CRM Proc. Lecture Notes 49, AMS, (2009), 1-44.

    [5]

    P. Biran and O. Cornea, Rigidity and uniruling for Lagrangian submanifolds, Geom. Topol., 13 (2009), 2881-2989.doi: doi:10.2140/gt.2009.13.2881.

    [6]

    Yu. V. Chekanov, Lagrangian tori in a symplectic vector space and global symplectomorphisms, Math. Z., 223 (1996), 547-559.

    [7]

    Yu. V. Chekanov, Lagrangian intersections, symplectic energy, and areas of holomorphic curves, Duke Math. J., 95 (1998), 213-226.doi: doi:10.1215/S0012-7094-98-09506-0.

    [8]

    Yu. Chekanov and F. SchlenkTwist tori I: Construction and classification, in preparation.

    [9]

    Yu. Chekanov and F. SchlenkTwist tori II: Non-displaceability, in preparation.

    [10]

    C.-H. Cho, Holomorphic discs, spin structures, and Floer cohomology of the Clifford torus, Int. Math. Res. Not., 35 (2004), 1803-1843.doi: doi:10.1155/S1073792804132716.

    [11]

    D. Eisenbud, "Commutative Algebra. With a View Toward Algebraic Geometry," Graduate Texts in Mathematics 150, Springer-Verlag, New York, 1995.

    [12]

    Ya. Eliashberg and L. Polterovich, The problem of Lagrangian knots in four-manifolds, in "Geometric Topology (Athens, GA, 1993)," AMS/IP Stud. Adv. Math. 2.1, AMS, (1997), 313-327.

    [13]

    Ya. Eliashberg and L. PolterovichSymplectic quasi-states on the quadric surface and Lagrangian submanifolds, arXiv:1006.2501.

    [14]

    M. Entov and L. Polterovich, Rigid subsets of symplectic manifolds, Compos. Math., 145 (2009), 773-826.doi: doi:10.1112/S0010437X0900400X.

    [15]

    A. Floer, Morse theory for Lagrangian intersections, J. Differential Geom., 28 (1988), 513-547.

    [16]

    K. Fukaya, Y.-G. Oh, H. Ohta and K. Ono, "Lagrangian Intersection Floer Theory: Anomaly and Obstruction. Part I," AMS/IP Studies in Advanced Mathematics 46.1, AMS, International Press, Somerville, MA, 2009.

    [17]

    K. Fukaya, Y.-G. Oh, H. Ohta and K. Ono, "Lagrangian Intersection Floer Theory: Anomaly and Obstruction. Part II," AMS/IP Studies in Advanced Mathematics 46.2, AMS, International Press, Somerville, MA, 2009.

    [18]

    K. Fukaya, Y.-G. Oh, H. Ohta and K. OnoToric degeneration and non-displaceable Lagrangian tori in $S^2 \times S^2$, arXiv:1002.1660.

    [19]

    A. GadbledExotic Hamiltonian tori in $\CP^2$ and $S^2 \times S^2$, in preparation.

    [20]

    M. Gromov, Pseudo-holomorphic curves in symplectic manifolds, Invent. math., 82 (1985), 307-347.

    [21]

    H. Hofer, On the topological properties of symplectic maps, Proc. Roy. Soc. Edinburgh Sect. A , 115 (1990), 25-38.

    [22]

    C. Weibel, "An Introduction to Homological Algebra," Cambridge Studies in Advanced Mathematics 38, Cambridge University Press, Cambridge, 1994.

  • 加载中
SHARE

Article Metrics

HTML views() PDF downloads(266) Cited by(0)

Access History

Other Articles By Authors

Catalog

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return