Quantum Kirwan map and quantum Steenrod operation

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.