Abstract
We describe the relationship between two spaces associated to a quiver with potential. The first is a complex manifold parametrizing Bridgeland stability conditions on a triangulated category, and the second is a cluster variety with a natural Poisson structure. For quivers of type A, we construct a local biholomorphism from the space of stability conditions to the cluster variety. The existence of this map follows from results of Sibuya in the classical theory of ordinary differential equations.
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