Abstract

An exact CY structure is a special kind of smooth CY structure in the sense of Kontsevich-Vlassopoulos. When the wrapped Fukaya category of a Weinstein manifold admits an exact CY structure, there is an induced cohomology class in its 1st degree S^1-equivariant symplectic cohomology, which, under the marking map, goes to an invertible element in the deg 0 (ordinary) symplectic cohomology. This generalizes the notion of a (quasi-) dilation introduced earlier by Seidel-Solomon. We show that one can define q-intersection numbers between simply-connected Lagrangian submanifolds in Weinstein manifolds with exact CY wrapped Fukaya categories and prove that there can be only finitely many disjoint Lagrangian spheres in these manifolds. The simplest non-trivial example of a Weinstein manifold whose wrapped Fukaya category is exact CY but which does not admit a quasi-dilation is the Milnor fiber of a 3-fold triple point studied previously by Smith-Thomas.