Symplectic Dynamics/Geometry Seminar

An exact Calabi-Yau structure, originally introduced by Keller, is a special kind of smooth Calabi-Yau structures in the sense of Kontsevich-Vlassopoulos. For a Weinstein manifold, an exact Calabi-Yau structure on the wrapped Fukaya category induces a class in the degree one equivariant symplectic cohomology, which we call a cyclic dilation. We prove that for many Weinstein manifolds with cyclic dilations, there is an upper bound on the number of pairwise disjoint Lagrangian spheres, and the homology classes of these Lagrangian spheres are non-trivial. On the other hand, we show that the Milnor fiber of a 3-fold triple point admits a cyclic dilation despite that there is no quasi-dilation.