On the Rim Tori Refinement of Relative Gromov-Witten Invariants

TL;DR

This paper develops a refined version of relative Gromov-Witten invariants using abelian covers, providing new insights and vanishing results, and discusses its implications for the symplectic sum formula.

Contribution

It introduces a novel refinement of relative Gromov-Witten invariants based on abelian covers, enhancing the understanding of their properties and applications.

Findings

Constructed Ionel-Parker's refinement using abelian covers

Derived vanishing results for standard invariants

Analyzed the refinement's impact on the symplectic sum formula

Abstract

We construct Ionel-Parker's proposed refinement of the standard relative Gromov-Witten invariants in terms of abelian covers of the symplectic divisor and discuss in what sense it gives rise to invariants. We use it to obtain some vanishing results for the standard relative Gromov-Witten invariants. In a separate paper, we describe to what extent this refinement sharpens the usual symplectic sum formula and give further qualitative applications.