# Intersections of $\omega$ classes in $\overline{\mathcal{M}}_{g,n}$

## TL;DR

This paper introduces a graph-based formula to express monomials in omega classes on moduli spaces of curves, linking them to simpler dual graphs and deriving new combinatorial formulas for intersection numbers.

## Contribution

It provides a novel graph formula for omega class monomials and relates top intersections of kappa classes to psi classes on moduli spaces.

## Key findings

- Graph formula for omega class monomials using dual graphs
- Expresses top kappa intersections in terms of psi class intersections
- Derives numerical and combinatorial consequences for intersection theory

## Abstract

We provide a graph formula which describes an arbitrary monomial in {\omega} classes (also referred to as stable {\psi} classes) in terms of a simple family of dual graphs (pinwheel graphs) with edges decorated by rational functions in {\psi} classes. We deduce some numerical consequences and in particular a combinatorial formula expressing top intersections of \k{appa} classes on Mg in terms of top intersections of {\psi} classes.