Symplectic structures with non-isomorphic primitive cohomology on open 4-manifolds

Author:

Gibson Matthew,Tseng Li-Sheng,Vidussi Stefano

Abstract

We analyze four-dimensional symplectic manifolds of type X = S 1 × M 3 X=S^1 \times M^3 where M 3 M^3 is an open 3 3 -manifold admitting inequivalent fibrations leading to inequivalent symplectic structures on X X . For the case where M 3 S 3 M^3 \subset S^3 is the complement of a 4 4 -component link constructed by McMullen-Taubes, 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 X . We also calculate the primitive cohomologies on X X for a class of open 3 3 -manifolds that are complements of a family of fibered graph links in S 3 S^3 . In this case, we show that there exist pairs of symplectic forms on X X , arising from either equivalent or inequivalent pairs of fibrations on the link complement, that have different dimensions of the primitive cohomologies.

Funder

Simons Foundation

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Reference11 articles.

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2. SnapPy, a computer program for studying the geometry and topology of 3-manifolds;Culler, M.

3. Annals of Mathematics Studies;Eisenbud, David,1985

4. Princeton Mathematical Series;Farb, Benson,2012

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