Airy structures and deformations of curves in surfaces

Abstract

An embedded curve in a symplectic surface (Formula presented.) defines a smooth deformation space (Formula presented.) of nearby embedded curves. A key idea of Kontsevich and Soibelman is to equip the symplectic surface (Formula presented.) with a foliation in order to study the deformation space (Formula presented.). The foliation, together with a vector space (Formula presented.) of meromorphic differentials on (Formula presented.), endows an embedded curve (Formula presented.) with the structure of the initial data of topological recursion, which defines a collection of symmetric tensors on (Formula presented.). Kontsevich and Soibelman define an Airy structure on (Formula presented.) to ..