Quantum cohomology as a deformation of symplectic cohomology

TL;DR

This paper demonstrates that quantum cohomology can be viewed as a deformation of symplectic cohomology in certain symplectic manifolds, and establishes rigidity results for the divisor complement's skeleton.

Contribution

It introduces a novel relationship between quantum and symplectic cohomology via deformation theory in specific symplectic manifolds.

Findings

Quantum cohomology deforms symplectic cohomology under certain conditions.

Rigidity results are established for the skeleton of the divisor complement.

The work applies to positively monotone compact symplectic manifolds.

Abstract

We prove that under certain conditions, the quantum cohomology of a positively monotone compact symplectic manifold is a deformation of the symplectic cohomology of the complement of a simple crossings symplectic divisor. We also prove rigidity results for the skeleton of the divisor complement.