Topological recursion for symplectic volumes of moduli spaces of curves

2010/10/08 by Julia Bennett, David Cochran, Bennett, Julia +5
Mathematics · Physics and Astronomy · #Algebraic Geometry (math.AG) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Symplectic Geometry (math.SG) #math-ph #math.AG #math.MP #math.SG

paper · pdf · doi:10.48550/arxiv.1010.1747

v2 - Clarified procedure used to calculate volumes using symplectic reduction (section 2.4). v3 - minor edits

arxiv created 2011/03/17 · arxiv updated 2011/03/18

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 = y² / 2.

Related

• Airy structures and symplectic geometry of topological recursion
• Seiberg-Witten Theory and Topological Recursion
• String and dilaton equations for counting lattice points in the moduli space of curves
• Cutting directed ribbon graphs and recursion for volumes of the combinatorial moduli spaces
• Volumes of moduli spaces of directed ribbon graphs and Cut-and-Join operators