Floer theory and flips

Abstract

We show that blow-ups or reverse flips (in the sense of the minimal model program) of rational symplectic manifolds with point centers create Floer-non-trivial Lagrangian tori. As applications, we demonstrate the existence of Hamiltonian non-displaceable Lagrangian tori in, for example, small symplectic blow-ups of compact symplectic manifolds and moduli spaces of polygons. These results are part of a conjectural description of generators for the Fukaya category of a compact symplectic manifold with a singularity-free running of the minimal model program.

171 pages, 38 figures. Minor corrections in response to proofs. arXiv admin note: text overlap with arXiv:1505.08146

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• $T$-equivariant disc potentials for toric Calabi-Yau manifolds
• Wall-crossing from Lagrangian Cobordisms
• Disjoinable Lagrangian tori and semisimple symplectic cohomology
• Holomorphic disks and the disk potential for a fibered Lagrangian
• Morse complexes and multiplicative structures
• Displacement energy of Lagrangian 3-spheres