Cobordism-valued intersection theory on $\overline{\mathcal{M}}_{0,n}$

TL;DR

This paper extends intersection theory on the moduli space of genus zero curves to algebraic cobordism, providing new inductive formulas for cobordism-valued psi-class intersections and explicit calculations up to n=8.

Contribution

It refines the string equation from Chow ring to algebraic cobordism, enabling computation of cobordism-valued Gromov-Witten invariants and classes on ,n.

Findings

Derived inductive formulas for cobordism-valued psi-class intersections

Computed cobordism classes ,n explicitly for n up to 8

Extended intersection theory to algebraic cobordism on ,n

Abstract

We calculate the genus zero cobordism-valued Gromov-Witten invariants of a point by refining the string equation on $\overline{\mathcal{M}}_{0,n}$ from the Chow ring to algebraic cobordism. This gives inductive formulas for cobordism-valued psi-class intersections on $\overline{\mathcal{M}}_{0,n}$, and in particular the cobordism classes $[\overline{\mathcal{M}}_{0,n}]$, and for their images in $K$-theory. Explicit formulas are given up to $n = 8$.