NCSGS - Divisor Complements in Calabi-Yau Symplectic Manifolds

Let (M, ω) be a closed symplectic manifold. Consider a closed symplectic submanifold D whose homology class is a positive multiple of the Poincare dual of [ω]. The complement of D can be given the structure of a Liouville manifold, with skeleton S. We prove that S cannot be displaced from itself inside M by a Hamiltonian isotopy if we assume that c1(M) = 0. Under the same assumption, we also prove that Floer theoretically essential Lagrangians in M have to intersect S. These results are related to an understanding of the notions heavy and superheavy in terms of relative symplectic cohomology. Ongoing joint work with Dmitry Tonkonog.