On the homological algebra of relative symplectic geometry

Abstract

This note discusses certain deformation theoretic aspects of the symplectic topology of pairs $(Y,D)$, where $Y$ is a smooth projective variety and $D$ is an ample simple normal crossings divisor. Motivated by homological mirror symmetry, we formulate a precise prediction concerning the symplectic cohomology of the affine variety $Y \setminus D$ for a wide class of examples. We show how our answer unites various mirror symmetry predictions in the literature.