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Composition Formula of Smooth Correspondences

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Kuranishi Structures and Virtual Fundamental Chains

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Abstract

The purpose of this chapter is to prove [FOOO8, Lemma 12.15] = Theorem 10.21, where a fiber product of Kuranishi structures is used as a way to define the composition of smooth correspondences. For this purpose we work out the plan described in Sect. 6.5 in the de Rham model.

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Notes

  1. 1.

    Here we do not use the fiber product orientation as \((X_2,Z_2,\widehat {\mathcal U_2},\widehat {\mathfrak S_2}) \,{ }_{\widehat {f_2}} \times _{\widehat {f_1}}\,\, (X_1,Z_1,\widehat {\mathcal U_1},\widehat {\mathfrak S_1})\).

References

  1. K. Fukaya, Y.-G. Oh, H. Ohta, K. Ono, Lagrangian Floer theory on compact toric manifolds II : Bulk deformations. Sel. Math. New Ser. 17, 609–711 (2011)

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Authors and Affiliations

  1. Simons Center for Geometry and Physics, State University of New York, Stony Brook, NY, USA

    Kenji Fukaya

  2. IBS Center for Geometry and Physics Pohang, Gyung-Buk, Korea

    Yong-Geun Oh

  3. Department of Mathematics, Postech Pohang, Gyung-Buk, Korea

    Yong-Geun Oh

  4. Graduate School of Mathematics Nagoya University, Nagoya, Japan

    Hiroshi Ohta

  5. Research Institute for Mathematical Sciences, Kyoto University, Kyoto, Japan

    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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Fukaya, K., Oh, YG., Ohta, H., Ono, K. (2020). Composition Formula of Smooth Correspondences. In: Kuranishi Structures and Virtual Fundamental Chains. Springer Monographs in Mathematics. Springer, Singapore. https://doi.org/10.1007/978-981-15-5562-6_10

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