Kyoto Journal of Mathematics

Seidel’s long exact sequence on Calabi-Yau manifolds

Yong-Geun Oh

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In this paper, we generalize construction of Seidel’s long exact sequence of Lagrangian Floer cohomology to that of compact Lagrangian submanifolds with vanishing Malsov class on general Calabi-Yau manifolds. We use the framework of anchored Lagrangian submanifolds and some compactness theorem of smooth J-holomorphic sections of Lefschetz Hamiltonian fibration for a generic choice of J. The proof of the latter compactness theorem involves a study of proper pseudoholomorphic curves in the setting of noncompact symplectic manifolds with cylindrical ends.

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Kyoto J. Math., Volume 51, Number 3 (2011), 687-765.

First available in Project Euclid: 1 August 2011

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Zentralblatt MATH identifier

Primary: 53D37: Mirror symmetry, symplectic aspects; homological mirror symmetry; Fukaya category [See also 14J33] 53D40: Floer homology and cohomology, symplectic aspects


Oh, Yong-Geun. Seidel’s long exact sequence on Calabi-Yau manifolds. Kyoto J. Math. 51 (2011), no. 3, 687--765. doi:10.1215/21562261-1299936.

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