The Quantum Orbifold Cohomology of Toric Stack Bundles

TL;DR

This paper constructs an explicit slice of Givental's Lagrangian cone for the quantum orbifold cohomology of toric stack bundles, linking the I-function to genus 0 Gromov-Witten invariants.

Contribution

It provides an explicit description of the Lagrangian cone in the quantum cohomology of toric stack bundles using the I-function.

Findings

The I-function lies on the Lagrangian cone for the quantum orbifold cohomology.

The construction applies to genus 0 Gromov-Witten theory of toric stack bundles.

The approach clarifies the relationship between the I-function and Gromov-Witten invariants.

Abstract

We study Givental's Lagrangian cone for the quantum orbifold cohomology of toric stack bundles and prove that the I-function gives points in the Lagrangian cone, namely we construct an explicit slice of the Lagrangian cone defined by the genus $0$ Gromov-Witten theory of a toric stack bundle.