A new spin on polynomial relations among kappa classes

TL;DR

This paper proves a conjecture about universal polynomial relations among kappa classes on moduli spaces of algebraic curves, using advanced techniques from spin Gromov-Witten theory and topological recursion.

Contribution

It establishes a new proof of polynomial relations among kappa classes, connecting spin Gromov-Witten theory with moduli space geometry.

Findings

Proves a conjecture on polynomial relations among kappa classes.

Utilizes localization and materialization analysis in spin Gromov-Witten theory.

Employs $ ext{Z}_2$-equivariant topological recursion.

Abstract

We prove a recent conjecture of the fourth named author with P. Norbury that states a system of universal polynomial relations among the kappa classes on the moduli spaces of algebraic curves. The proof involves localization and materialization analysis of the spin Gromov-Witten theory of the projective line and is dictated by $\mathbb{Z}_2$-equivariant topological recursion.