S¹-equivariant Rabinowitz-Floer homology

2013/12/18 by Frauenfelder, Urs, Schlenk, Felix
#53D40 #FOS: Mathematics #Symplectic Geometry (math.SG)

paper · doi:10.48550/arxiv.1312.5201

Abstract

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 \widehat M_J 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 \widehat M_J that turns out to be compact for small enough perturbations.

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