1312.5201Dec 18, 201344 pages, 4 figures, Main body of the paper to appear in the Hokkaido Mathematical Journal. The new appendix describes an approach to transversality for Floer homologies for which one has compactness a priori. A more detailed account of this appendix is under construction
We define the S1-equivariant Rabinowitz-Floer homology of a bounding contact hypersurface Σ in an exact symplectic manifold, and show by a geometric argument that it vanishes if Σ is displaceable. In the appendix we describe an approach to transversality for Floer homologies for which the moduli space MJ
Nearby in the stack
of all gradient flow lines is compact for some almost complex structure
J
. This approach uses a large set of perturbations, namely vector fields on the loop space, and selects from the possibly non-compact perturbed moduli spaces a part near
MJ
that turns out to be compact for small enough perturbations.