Quantum Kirwan map and quantum Steenrod operation

TL;DR

This paper develops an equivariant extension of the quantum Kirwan map, linking classical and quantum Steenrod operations, and resolves a conjecture in the monotone symplectic setting.

Contribution

It introduces a new equivariant quantum Kirwan map that connects classical and quantum Steenrod operations, advancing the understanding of symplectic reductions.

Findings

Constructed an equivariant quantum Kirwan map.

Proved the map intertwines classical and quantum Steenrod operations.

Resolved the monotone case of Salamon's quantum Kirwan map conjecture.

Abstract

We construct an equivariant extension of the quantum Kirwan map and show that it intertwines the classical Steenrod operation on the cohomology of a classifying space with the quantum Steenrod operation of a monotone symplectic reduction. This provides a new method of computing quantum Steenrod operations developed by Seidel-Wilkins. When specialized to the non-equivariant piece, our result also resolves the monotone case of Salamon's quantum Kirwan map conjecture in the symplectic setting.