On Gromov--Witten invariants of $\mathbb{P}^1$

TL;DR

This paper proposes a conjectural explicit formula for generating series of Gromov--Witten invariants of the projective line across all degrees and genera, aiming to deepen understanding of these enumerative invariants.

Contribution

It introduces a new conjectural explicit formula for the generating series of Gromov--Witten invariants of b^1 for all degrees and genera, advancing theoretical understanding.

Findings

Proposed a conjectural explicit formula for generating series.

Covered all degrees and genera in the invariants.

Aimed to facilitate future computations and theoretical insights.

Abstract

We propose a conjectural explicit formula of generating series of a new type for Gromov--Witten invariants of $\mathbb{P}^1$ of all degrees in full genera.