# Mirror of Atiyah flop in symplectic geometry and stability conditions

## TL;DR

This paper explores the mirror of the Atiyah flop within symplectic geometry, establishing a formulation for symplectic manifolds with Lagrangian fibrations and analyzing the impact on stability conditions in the Fukaya category.

## Contribution

It introduces a formulation of the mirror Atiyah flop in symplectic geometry and constructs stability conditions on the derived Fukaya category of the deformed conifold.

## Key findings

- Formulation of the mirror Atiyah flop for symplectic manifolds with Lagrangian fibrations
- Construction of geometric stability conditions on the Fukaya category
- Analysis of the flop's action on 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.