Rabinowitz Floer homology and symplectic homology

Abstract

The first two authors have recently defined Rabinowitz Floer homology groups RFH*(M, W) associated to a separating exact embedding of a contact manifold (M, ξ) into a symplectic manifold (W,ω). These depend only on the bounded component V of W \ M. We construct a long exact sequence in which symplectic cohomology of V maps to symplectic homology of V, which in turn maps to Rabinowitz Floer homology RFH*(M, W), which then maps to symplectic cohomology of V. We compute RFH *(ST*L, T*L), where ST *L is the unit cosphere bundle of a closed manifold L. As an application, we prove that the image of a separating exact contact embedding of ST*L cannot be displaced away from itself by a Hamiltonian isotopy, provided dim L ≥ 4 and the embedding induces an injection on π1.