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Fibered Symplectic Cohomology and the Leray-Serre Spectral Sequence

Alexandru Oancea
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Abstract

We define Symplectic cohomology groups for a class of symplectic fibrations with closed symplectic base and convex at infinity fiber. The crucial geometric assumption on the fibration is a negativity property reminiscent of negative curvature in complex vector bundles. When the base is symplectically aspherical we construct a spectral sequence of Leray-Serre type converging to the Symplectic cohomology groups of the total space, and we use it to prove new cases of the Weinstein conjecture.

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Alexandru Oancea. 2007-07-24. Fibered Symplectic Cohomology and the Leray-Serre Spectral Sequence. https://arxiv.org/abs/math/0503193

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