Surveys in Differential Geometry

Volume 17 (2012)

Lagrangian Floer theory on compact toric manifolds: A survey

Pages: 229 – 298

DOI: http://dx.doi.org/10.4310/SDG.2012.v17.n1.a6

Authors

Kenji Fukaya (Department of Mathematics, Kyoto University, Kyoto, Japan.)

Yong-Geun Oh (Department of Mathematics, University of Wisconsin, Madison, Wisc, U.S.A.; Department of Mathematics, POSTECH, Pohang, Korea.)

Hiroshi Ohta (Graduate School of Mathematics, Nagoya University, Nagoya, Japan; Korea Institute for Advanced Study, Seoul, Korea)

Kaoru Ono (Department of Mathematics, Hokkaido University, Sapporo, Japan; Korea Institute for Advanced Study, Seoul, Korea)

Abstract

This article is a survey of the Lagrangian Floer theory of toric manifolds, which summarizes the results obtained in a series of the present authors’ papers. In this survey, we discuss calculations of the Floer cohomology of Lagrangian T orbits in compact toric manifolds. Applications to symplectic topology and to mirror symmetry are also discussed.

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