Floer cohomology of torus fibers and real lagrangians in Fano toric manifolds

Details Floer cohomology of torus fibers and real lagrangians in Fano toric manifolds Floer cohomology of torus fibers and real lagrangians in Fano toric manifolds

2010-03-18

arxiv.org/abs/1003.3651v3

Mathematics

Symplectic Geometry

v2: Modified exposition and new corollary added

Scientific paper

In this article, we consider the Floer cohomology (with $\Z_2$ coefficients) between torus fibers and the real Lagrangian in Fano toric manifolds. We first investigate the conditions under which the Floer cohomology is defined, and then develop a combinatorial description of the Floer complex based on the polytope of the toric manifold. We show that if the Floer cohomology is defined, and the Floer cohomology of the torus fiber is non-zero, then the Floer cohomology of the pair is non-zero. We use this result to develop some applications to non-displaceability and the minimum number of intersection points under Hamiltonian isotopy.

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