SYMPLECTIC STRUCTURES WITH NON-ISOMORPHIC PRIMITIVE COHOMOLOGY ON OPEN 4-MANIFOLDS

We analyze four-dimensional symplectic manifolds of type X = S1 x M3 where M3 is an open 3-manifold admitting inequivalent fibrations leading to inequivalent symplectic structures on X. For the case where M3 subset of S3 is the complement of a 4-component link constructed by McMullen-Taub es, we provide a general algorithm for computing the monodromy of the fibrations explicitly. We use this algorithm to show that certain inequivalent symplectic structures are distinguished by the dimensions of the primitive cohomologies of differential forms on X. We also calculate the primitive cohomologies on X for a class of open 3-manifolds that are complements of a family of fibered graph links in S3. In this case, we show that there exist pairs of symplectic forms on X, arising from either equivalent or inequivalent pairs of fibrations on the link complement, that have different dimensions of the primitive cohomologies.