Cohomological field theories with non-tautological classes

TL;DR

This paper introduces a new method for constructing Cohomological Field Theories with units using minimal classes, revealing examples that extend beyond tautological cohomology on moduli spaces of curves.

Contribution

It develops a novel approach to build CohFTs with units from minimal classes, including examples outside the tautological cohomology.

Findings

Constructed CohFTs with units outside tautological cohomology

Developed a method using minimal classes on moduli spaces

Analyzed minimal classes in low genus cases

Abstract

A method of constructing Cohomological Field Theories (CohFTs) with unit using minimal classes on the moduli spaces of curves is developed. As a simple consequence, CohFTs with unit are found which take values outside of the tautological cohomology of the moduli spaces of curves. A study of minimal classes in low genus is presented in the Appendix by D. Petersen.