Products of Floer cohomology of torus fibers in toric Fano manifolds

Cheol-Hyun Cho

Symplectic Geometry mathscidoc:1912.43238

Communications in mathematical physics, 260, (3), 613-640, 2005.12
We compute the ring structure of Floer cohomology groups of Lagrangian torus fibers in some toric Fano manifolds continuing the study of [CO]. Related <i>A</i><sub></sub>-formulas hold for a transversal choice of chains. Two different computations are provided: a direct calculation using the classification of holomorphic discs by Oh and the author in [CO], and another method by using an <i>analogue of divisor equation</i> in Gromov-Witten invariants to the case of discs. Floer cohomology rings are shown to be isomorphic to Clifford algebras, whose quadratic forms are given by the Hessians of functions <i>W</i>, which turn out to be the superpotentials of Landau-Ginzburg mirrors. In the case of , this proves the prediction made by Hori, Kapustin and Li by B-model calculations via physical arguments. The latter method also provides correspondence between higher derivatives of the superpotential of LG mirror with
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@inproceedings{cheol-hyun2005products,
  title={Products of Floer cohomology of torus fibers in toric Fano manifolds},
  author={Cheol-Hyun Cho},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191221113120110742798},
  booktitle={Communications in mathematical physics},
  volume={260},
  number={3},
  pages={613-640},
  year={2005},
}
Cheol-Hyun Cho. Products of Floer cohomology of torus fibers in toric Fano manifolds. 2005. Vol. 260. In Communications in mathematical physics. pp.613-640. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191221113120110742798.
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