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.
Bibliographical noteFunding Information:
We express our gratitude to Matthew Young for drawing our attention to the work of Nagao and Nakajima, and Yukinobu Toda for helpful discussions. S.-C. Lau expresses his gratitude for the AMS-Simons Travel Grant. The work of H. Hong and S.-T. Yau is substantially supported by Simons Collaboration Grant on Homological Mirror Symmetry.
All Science Journal Classification (ASJC) codes
- Physics and Astronomy(all)