Seidel's long exact sequence on Calabi-Yau manifolds

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.Comment: 59 pages, comments welcom

Floer homology and its continuity for non-compact Lagrangian submanifolds

We give a construction of the Floer homology of the pair of {\it non-compact} Lagrangian submanifolds, which satisfies natural continuity property under the Hamiltonian isotopy which moves the infinity but leaves the intersection set of the pair compact. This construction uses the concept of Lagrangian cobordism and certain singular Lagrangian submanifolds. We apply this construction to conormal bundles (or varieties) in the cotangent bundle, and relate it to a conjecture made by MacPherson on the intersection theory of the characteristic Lagrangian cycles associated to the perverse sheaves constructible to a complex stratification on the complex algebraic manifold.Comment: Submitted to the Proceedings for 7th Gokova Geometry-Topology Conferenc

Chain level Floer theory and Hofer's geometry of the Hamiltonian diffeomorphism group

In this paper we first apply the chain level Floer theory to the study of Hofer's geometry of Hamiltonian diffeomorphism group in the cases without quantum contribution: we prove that any quasi-autonomous Hamiltonian path on weakly exact symplectic manifolds or any autonomous Hamiltonian path on arbitrary symplectic manifolds is length minimizing in its homotopy class with fixed ends, as long as it has a fixed maximum and a fixed minimum which are not over-twisted and all of its contractible periodic orbits of period less than one are sufficiently $C^1$-small. Next we give a construction of new invariant norm of Viterbo's type on the Hamiltonian diffeomorphism group of arbitrary compact symplectic manifolds.Comment: Section 6 concerning adic (or adiabadic) limit of Floer's moduli space is removed and so sections and proofs are reorganize