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Lagrangian Floer theory on compact toric manifolds II: bulk deformations

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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.

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Authors and Affiliations

  1. Department of Mathematics, Kyoto University, Kitashirakawa, Kyoto, 606-8502, Japan

    Kenji Fukaya

  2. Department of Mathematics, University of Wisconsin, Madison, WI, USA

    Yong-Geun Oh

  3. Graduate School of Mathematics, Nagoya University, Chikusa, Nagoya, 464-8602, Japan

    Hiroshi Ohta

  4. Department of Mathematics, Hokkaido University, Sapporo, 060-0810, Japan

    Kaoru Ono

  5. Korea Institute for Advanced Study, Seoul, Korea

    Hiroshi Ohta & Kaoru Ono

Authors
  1. Kenji Fukaya
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  2. Yong-Geun Oh
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  3. Hiroshi Ohta
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  4. Kaoru Ono
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Corresponding author

Correspondence to Kenji Fukaya.

Additional information

KF is supported partially by JSPS Grant-in-Aid for Scientific Research No.18104001 and by Global COE Program G08, YO by US NSF grant # 0904197, HO by JSPS Grant-in-Aid for Scientific Research No.19340017, and KO by JSPS Grant-in-Aid for Scientific Research, Nos. 18340014 and 21244002.

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Fukaya, K., Oh, YG., Ohta, H. et al. Lagrangian Floer theory on compact toric manifolds II: bulk deformations. Sel. Math. New Ser. 17, 609–711 (2011). https://doi.org/10.1007/s00029-011-0057-z

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