Mirror of Atiyah flop in symplectic geometry and stability conditions

Abstract

We study the mirror operation of the Atiyah flop in symplectic geometry. We formulate the operation for a symplectic manifold with a Lagrangian fibration. Furthermore we construct geometric stability conditions on the derived Fukaya category of the deformed conifold and study the action of the mirror Atiyah flop on these stability conditions.

arXiv commentv2: 45 pages, 18 figures; revised exposition