Selecta Mathematica

, 17:609

Lagrangian Floer theory on compact toric manifolds II: bulk deformations


    • Department of MathematicsKyoto University
  • Yong-Geun Oh
    • Department of MathematicsUniversity of Wisconsin
  • Hiroshi Ohta
    • Graduate School of MathematicsNagoya University
    • Korea Institute for Advanced Study
  • Kaoru Ono
    • Department of MathematicsHokkaido University
    • Korea Institute for Advanced Study

DOI: 10.1007/s00029-011-0057-z

Cite this article as:
Fukaya, K., Oh, Y., Ohta, H. et al. Sel. Math. New Ser. (2011) 17: 609. doi:10.1007/s00029-011-0057-z


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.


Toric manifoldsFloer cohomologyWeakly unobstructed Lagrangian submanifoldsPotential functionJacobian ringBulk deformationsBulk-balanced Lagrangian submanifoldsOpen-closed Gromov-Witten invariant

Mathematics Subject Classification (2000)

Primary 53D1253D40Secondary 53D3514M25
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© Springer Basel AG 2011