Floer theory and flips

2015/08/07 by Charest, François, Woodward, Chris T. · 1 citation
#53D40 #FOS: Mathematics #Symplectic Geometry (math.SG)

paper · doi:10.48550/arxiv.1508.01573

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.

Cited by

• Mirror construction of Hecke correspondence between Nakajima quiver varieties
• Fukaya algebras via stabilizing divisors

Related

• Lagrangian Floer theory on Woodward's multiplicity-free U(2)-manifolds
• Lagrangian Floer theory, from geometry to algebra and back again
• Lagrangian Non-Intersections
• Lagrangian Floer theory over integers: spherically positive symplectic manifolds
• Localized mirror functor constructed from a Lagrangian torus