An exact sequence for contact- and symplectic homology

A symplectic manifold W with contact type boundary M=a,W induces a linearization of the contact homology of M with corresponding linearized contact homology HC(M). We establish a Gysin-type exact sequence in which the symplectic homology SH(W) of W maps to HC(M), which in turn maps to HC(M), by a map of degree -2, which then maps to SH(W). Furthermore, we give a description of the degree -2 map in terms of rational holomorphic curves with constrained asymptotic markers, in the symplectization of M.