## Kyoto Journal of Mathematics

### Seidel’s long exact sequence on Calabi-Yau manifolds

Yong-Geun Oh

#### Abstract

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.

#### Article information

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

Dates
First available in Project Euclid: 1 August 2011

https://projecteuclid.org/euclid.kjm/1312205244

Digital Object Identifier
doi:10.1215/21562261-1299936

Mathematical Reviews number (MathSciNet)
MR2824005

Zentralblatt MATH identifier
1230.53079

#### Citation

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. https://projecteuclid.org/euclid.kjm/1312205244

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