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

Abstract

In this article, we consider the Floer cohomology (with ${\mathbb{Z}}_2$ 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.

v2: Modified exposition and new corollary added

References in corpus (5)

• Rigid subsets of symplectic manifolds
• Rigidity and uniruling for Lagrangian submanifolds
• Non-displaceable Lagrangian submanifolds and Floer cohomology with non-unitary line bundle
• Microlocal condition for non-displaceablility
• Lagrangian Floer homology of the Clifford torus and real projective space in odd dimensions

Cited by in corpus (2)

• Quasi-morphisms on contactomorphism groups and contact rigidity
• Remarks on Lagrangian intersections in toric manifolds