529 research outputs found
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
Localization of Floer homology of engulfable topological Hamiltonian loop
Localization of Floer homology is first introduced by Floer
\cite{floer:fixed} in the context of Hamiltonian Floer homology. The author
employed the notion in the Lagrangian context for the pair of
compact Lagrangian submanifolds in tame symplectic manifolds in
\cite{oh:newton,oh:imrn} for a compact Lagrangian submanifold and
-small Hamiltonian . In this article, motivated by the study of
topological Hamiltonian dynamics, we extend the localization process for any
engulfable Hamiltonian path whose time-one map is
sufficiently -close to the identity (and also to the case of triangle
product), and prove that the value of local Lagrangian spectral invariant is
the same as that of global one. Such a Hamiltonian path naturally occurs as an
approximating sequence of engulfable topological Hamiltonian loop. We also
apply this localization to the graphs \Graph \phi_H^t in and localize the Hamiltonian Floer complex of such a
Hamiltonian . We expect that this study will play an important role in the
study of homotopy invariance of the spectral invariants of topological
Hamiltonian.Comment: 30http://arxiv.org/help/prep#comments pages, incorrect usage of area
in the localization process is replaced by the usage of maximum principle, a
coincidence theorem of local Lagrangian spectral invariants and the global
ones on cotangent bundle is added; v4) exposition improve
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