An exact sequence for contact- and symplectic homology
Résumé
Given a symplectic manifold $(W,\omega)$ with contact type boundary $(M,\xi)$, one can define the symplectic homology of $(W,\omega)$ and the linearized contact homology of $(M,\xi)$ with respect to its filling. We establish a Gysin-type exact sequence relating these invariants and describe one of the maps therein in terms of rational holomorphic curves in the symplectization of $(M,\xi)$.