Fibrancy of Symplectic Homology in Cotangent Bundles

摘要

We describe how the result in [Krall] 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 q?N, which will define a graded local coefficient system on N. The spectral sequence will then have page two isomorphic to homology of N with coefficients in this graded local system.