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.
|Number of pages||59|
|Journal||Advances in Theoretical and Mathematical Physics|
|Publication status||Published - 2018|
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.
© 2018 International Press of Boston, Inc.
All Science Journal Classification (ASJC) codes
- Physics and Astronomy(all)