The quantum equivariant cohomology of toric manifolds through mirror symmetry

TL;DR

This paper employs mirror symmetry to compute the quantum equivariant cohomology ring of toric manifolds, linking topological sigma-models and Hamiltonian Gromov-Witten invariants, providing new insights into their geometric structures.

Contribution

It introduces a method to explicitly calculate the quantum equivariant cohomology of toric manifolds using mirror symmetry, a novel approach in this context.

Findings

Explicit computation of quantum equivariant cohomology rings

Connection established between topological gauged sigma-models and Gromov-Witten invariants

Demonstration of mirror symmetry's utility in complex geometric calculations

Abstract

Using mirror symmetry as described by Hori and Vafa, we compute the quantum equivariant cohomology ring of toric manifolds. This ring arises naturally in topological gauged sigma-models and is related to the Hamiltonian Gromov-Witten invariants of the target manifold.