Topological recursion for open intersection numbers

2016/01/15 by Safnuk, Brad · 1 citation
#Algebraic Geometry (math.AG) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Symplectic Geometry (math.SG)

paper · doi:10.48550/arxiv.1601.04049

Abstract

We present a topological recursion formula for calculating the intersection numbers defined on the moduli space of open Riemann surfaces. The spectral curve is x = (1)/(2)y², the same as spectral curve used to calculate intersection numbers for closed Riemann surfaces, but the formula itself is a variation of the usual Eynard-Orantin recursion. It looks like the recursion formula used for spectral curves of degree 3, and also includes features present in β-deformed models. The recursion formula suggests a conjectural refinement to the generating function that allows for distinguishing intersection numbers on moduli spaces with different numbers of boundary components.

Cited by

• The identification of the extended refined open partition function and the Kontsevich-Penner matrix model

Related

• An effective recursion formula for computing intersection numbers
• Combinatorial models for moduli spaces of open Riemann surfaces
• Invariants of spectral curves and intersection theory of moduli spaces of complex curves
• Local topological recursion governs the enumeration of lattice points in \mathcal M_g,n
• Topological recursion on the Bessel curve