Floer Cohomology and Flips

Charest and Woodward 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. These results are part of a conjectural decomposition of the Fukaya category of a compact symplectic manifold with a singularly-free running of the minimal model program, they say, which is analogous to the description of Bondal-Orlav (Derived Categories of Coherent Sheaves, 2002) and Kawamata (Derived Categories of Toric Varieties, 2006) of the bounded derived category of coherent sheaves on a compact complex manifold.