Topological recursion for symplectic volumes of moduli spaces of curves

TL;DR

This paper develops a recursive approach to compute symplectic volumes of moduli spaces of curves using topological recursion, connecting symplectic geometry with combinatorial models and the Eynard-Orantin formalism.

Contribution

It introduces a new recursive formula for symplectic volumes via symplectic reduction and relates it to the Eynard-Orantin recursion for the Airy curve.

Findings

Recursive formula for symplectic volumes derived

Connection established between symplectic reduction and topological recursion

Eynard-Orantin recursion applied to moduli space volumes

Abstract

We construct locally defined symplectic torus actions on ribbon graph complexes. Symplectic reduction techniques allow for a recursive formula for the symplectic volumes of these spaces. Taking the Laplace transform results in the Eynard-Orantin recursion formulas for the Airy curve x = y^2 / 2.