On Gromov-Witten theory of projective bundles

TL;DR

This paper proves that the genus zero equivariant Gromov-Witten theories of projective bundles over GKM manifolds are isomorphic when the underlying vector bundles have identical equivariant Chern classes.

Contribution

It establishes a natural isomorphism between the Gromov-Witten theories of projective bundles derived from vector bundles with matching equivariant Chern classes.

Findings

Genus zero equivariant Gromov-Witten theories are isomorphic under the given conditions.

The result applies to projective bundles over GKM manifolds with equivariantly Chern class equivalence.

Provides a new understanding of the relationship between vector bundle invariants and Gromov-Witten theory.

Abstract

Given two equivariant vector bundles over an algebraic GKM manifold with the same equivariant Chern classes, we show that the genus zero equivariant Gromov--Witten theory of their projective bundles are naturally isomorphic.