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.
| Original language | English |
|---|---|
| Pages (from-to) | 1149-1207 |
| Number of pages | 59 |
| Journal | Advances in Theoretical and Mathematical Physics |
| Volume | 22 |
| Issue number | 5 |
| DOIs | |
| Publication status | Published - 2018 |
Bibliographical note
Funding 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.
Publisher Copyright:
© 2018 International Press of Boston, Inc.
All Science Journal Classification (ASJC) codes
- Mathematics(all)
- Physics and Astronomy(all)