UC Irvine

We study a symplectic cohomology defined on any symplectic manifold (X, w), introduced by Tseng and Yau. As a main application, we analyze two different fibrations of a link complement M constructed by McMullen-Taubes, and studied further by Vidussi. These examples lead to inequivalent symplectic forms on X = S1 x M, which can be distinguished by the dimension of the primitive cohomologies of differential forms. We provide a general algorithm for computing the monodromies of the fibrations explicitly, which are needed to determine the primitive cohomologies. We also investigate a similar phenomenon coming from fibrations of a class of graph links, whose primitive cohomology provides information about the fibration structure. We then study the A-infinity structure on the differential forms underlying the symplectic cohomology. We use this A-infinity structure to generalize classic notions such as Massey products and twisted differentials. These tools capture more information on certain symplectic 4-manifolds compared to the DGA structure on the de Rham cohomology of X.