Multipoint series of Gromov-Witten invariants of CP^1

TL;DR

This paper provides explicit formulas for the multipoint Gromov-Witten invariants of CP^1, utilizing Toda hierarchy recursions and equations to extend calculations across degrees, also deriving formulas for Hodge series.

Contribution

It introduces new explicit formulas for Gromov-Witten invariants of CP^1 using Toda hierarchy methods and extends calculations to higher degrees.

Findings

Formulas for multipoint Gromov-Witten invariants of CP^1

Recursion relations based on Toda hierarchy

Explicit Hodge series formulas for lambda_g and lambda_{g-1}

Abstract

We give explicit formulas for the multipoint series of Gromov-Witten invariants of CP^1. We use the recursions of the Toda hierarchy to calculate these in degree 0, and the Toda equation and the degree 0 formulas to extend the calculation to higher degrees. We also obtain formulas for the Hodge series for the Hodge classes lambda_g and lambda_{g-1}.