Fibrancy of Symplectic Homology in Cotangent Bundles

Abstract: We describe how the result in [1] extends to prove the existence of a Serre type spectral sequence converging to the symplectic homology SH_(M) of an exact Sub-Liouville domain M in a cotangent bundle T*N. We will define a notion of a fiber-wise symplectic homology SH_(M,q) for each point q in N, which will define a graded local coefficient system on N. The spectral sequence will then have page two isomorphic to the homology of N with coefficients in this graded local system.