A remark on virtual pushforward properties in Gromov-Witten theory

TL;DR

This paper explores virtual pushforward properties in Gromov-Witten theory using bivariant intersection theory, extending existing results to relate invariants of a projective bundle to those of its base.

Contribution

It extends Manolache's virtual pushforward result and applies it to connect relative and rubber Gromov-Witten invariants of a projective bundle with its base.

Findings

Extended virtual pushforward result of Manolache.

Derived relation between relative and rubber GW invariants.

Applied bivariant intersection theory to Gromov-Witten invariants.

Abstract

We approach Gathmann's virtual pushforward property from the perspective of bivariant intersection theory, extend a virtual pushforward result of Manolache, and use our extension to deduce a result of Gathmann relating relative and rubber GW invariants of a $P^1$ bundle with invariants of its base.