Airy structures and symplectic geometry of topological recursion

Understand

We propose a new approach to the topological recursion of Eynard-Orantin based on the notion of Airy structure, which we introduce in the paper.

• We explain why Airy structure is a more fundamental object than the one of the spectral curve.
• We explain how the concept of quantization of Airy structure leads naturally to the formulas of topological recursion as well as their generalizations.
• The notion of spectral curve is also considered in a more general framework of Poisson surfaces endowed with foliation.