Selecta Mathematica

, 17:609 | Cite as

Lagrangian Floer theory on compact toric manifolds II: bulk deformations

  • Kenji Fukaya
  • Yong-Geun Oh
  • Hiroshi Ohta
  • Kaoru Ono
Article

Abstract

This is a continuation of part I in the series of the papers on Lagrangian Floer theory on toric manifolds. Using the deformations of Floer cohomology by the ambient cycles, which we call bulk deformations, we find a continuum of non-displaceable Lagrangian fibers on some compact toric manifolds. We also provide a method of finding all fibers with non-vanishing Floer cohomology with bulk deformations in arbitrary compact toric manifolds, which we call bulk-balanced Lagrangian fibers.

Keywords

Toric manifolds Floer cohomology Weakly unobstructed Lagrangian submanifolds Potential function Jacobian ring Bulk deformations Bulk-balanced Lagrangian submanifolds Open-closed Gromov-Witten invariant 

Mathematics Subject Classification (2000)

Primary 53D12 53D40 Secondary 53D35 14M25 

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Copyright information

© Springer Basel AG 2011

Authors and Affiliations

  • Kenji Fukaya
    • 1
  • Yong-Geun Oh
    • 2
  • Hiroshi Ohta
    • 3
    • 5
  • Kaoru Ono
    • 4
    • 5
  1. 1.Department of MathematicsKyoto UniversityKyotoJapan
  2. 2.Department of MathematicsUniversity of WisconsinMadisonUSA
  3. 3.Graduate School of MathematicsNagoya UniversityNagoyaJapan
  4. 4.Department of MathematicsHokkaido UniversitySapporoJapan
  5. 5.Korea Institute for Advanced StudySeoulKorea

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