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Lagrangian Floer theory on compact toric manifolds II: bulk deformations

2011; Birkhäuser; Volume: 17; Issue: 3 Linguagem: Inglês

10.1007/s00029-011-0057-z

1420-9020

Kenji Fukaya, Yong‐Geun Oh, Hiroshi Ohta, Kaoru Ono,

Homotopy and Cohomology in Algebraic Topology

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.