Symplectic cohomology relative to a smooth anticanonical divisor

TL;DR

This paper computes a deformed version of symplectic cohomology for a monotone symplectic manifold with a smooth anticanonical divisor, incorporating intersections with the divisor, and describes its algebraic structures.

Contribution

It introduces and explicitly computes a formal deformation of symplectic cohomology accounting for divisor intersections, linking it to classical cohomology.

Findings

Deformed symplectic cohomology expressed in terms of ordinary cohomology.

Identification of additional algebraic structures on the deformed cohomology.

Explicit computation for the case of a smooth anticanonical divisor.

Abstract

For a monotone symplectic manifold and a smooth anticanonical divisor, there is a formal deformation of the symplectic cohomology of the divisor complement, defined by allowing Floer cylinders to intersect the divisor. We compute this deformed symplectic cohomology, in terms of the ordinary cohomology of the manifold and divisor; and also describe some additional structures that it carries.