Morphisms of CohFT algebras and quantization of the Kirwan map

TL;DR

This paper develops a new framework for morphisms of CohFT algebras inspired by A-infinity structures, and proposes a quantization of the Kirwan map linking equivariant and quotient quantum cohomologies, with applications to orbifold quantum cohomology.

Contribution

It introduces a novel notion of morphism for CohFT algebras and a quantization of the Kirwan morphism connecting equivariant and quotient quantum cohomologies.

Findings

Defined morphisms of CohFT algebras based on A-infinity analogy

Constructed a quantized Kirwan morphism for quantum cohomology

Identified Cartier divisors on moduli space of scaled marked curves

Abstract

We introduce a notion of morphism of CohFT algebras, based on the analogy with A-infinity morphisms. We discuss a "quantization" of the classical Kirwan morphism to a morphism of CohFT algebras from the equivariant quantum cohomology of a G-variety to the quantum cohomology of its git or symplectic quotient, and an example relating to the orbifold quantum cohomology of a compact toric orbifold. Finally we identify the space of Cartier divisors on the moduli space of scaled marked curves; these appear in the splitting axiom.