Analyticity and resurgence in wall-crossing formulas

Understand

We introduce the notion of analytic stability data on the Lie algebra of vector fields on a torus.

• We prove that the subspace of analytic stability data is open and closed in the topological space of all stability data.
• We formulate a general conjecture which explains how analytic stability data give rise to resurgent series.
• This conjecture is checked in several examples.