Gromov-Witten theory of target curves and the tautological ring

TL;DR

This paper proves that certain cohomology classes arising from Gromov-Witten invariants of target curves are contained within the tautological ring, linking enumerative geometry with algebraic structures on moduli spaces.

Contribution

It establishes that descendent integrals in Gromov-Witten theory of curves are always in the tautological ring, revealing a fundamental algebraic structure.

Findings

Cohomology classes from Gromov-Witten invariants lie in the tautological ring

Descendent integrals are contained within the tautological ring

Provides a structural understanding of Gromov-Witten classes for curves

Abstract

In the Gromov-Witten theory of a target curve we consider descendent integrals against the virtual fundamental class relative to the forgetful morphism to the moduli space of curves. We show that cohomology classes obtained in this way lie in the tautological ring.