In joint work with J. Rasmussen, we gave an interpretation of Heegaard Floer homology for manifolds torus boundary in terms immersed curves a punctured torus. particular, knot is captured by this invariant. Appealing to earlier the authors on bordered homology, give formula behaviour these under cabling.

The first two authors have recently defined RabinowitzFloer homology groups RFH∗(M,W ) associated to an 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∗...