# Higher genus relative Gromov--Witten theory and DR-cycles

## TL;DR

This paper extends the framework of relative Gromov--Witten invariants to all genera, demonstrating their structure as a partial CohFT and establishing new cycle relations on the moduli space of stable maps.

## Contribution

It introduces a generalized definition of relative Gromov--Witten invariants with negative contact orders for all genera and proves their partial CohFT structure.

## Key findings

- Relative Gromov--Witten invariants are extended to all genera.
- The theory forms a partial CohFT.
- New cycle relations on the moduli space of stable maps are established.

## Abstract

We extend the definition of relative Gromov--Witten invariants with negative contact orders to all genera. Then we show that relative Gromov--Witten theory forms a partial CohFT. Some cycle relations on the moduli space of stable maps are also proved.