Floer homology and its continuity for non-compact Lagrangian submanifolds

Details Floer homology and its continuity for non-compact Lagrangian submanifolds Floer homology and its continuity for non-compact Lagrangian submanifolds

2000-11-16

arxiv.org/abs/math/0011116v1

Turk. J. Math. 25 (2001) 103-124

Mathematics

Symplectic Geometry

Submitted to the Proceedings for 7th Gokova Geometry-Topology Conference

Scientific paper

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.

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