Calabi-Yau流形上的Seidel长exact sequence
Seidel's long exact sequence on Calabi-Yau manifolds
摘要：
本文将Seidel的Lagrangian Floer上同调长精确序列的构造推广到一般Calabi-Yau流形上Malsov类为零的紧拉格朗日子流形的构造.我们利用\cite{fooo:anchor}中发展的锚定拉格朗日子流形的框架和\emph{smooth}中的一些紧性定理$J$ -Lefschetz Hamilton纤维化的全纯截面来选择$J$。后一个紧性定理的证明涉及到在具有圆柱端点的非紧辛流形的背景下对真伪全纯曲线的研究。
英文摘要：
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 developed in \cite{fooo:anchor} and some compactness theorem of \emph{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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