Computing the Rabinowitz Floer homology of tentacular hyperboloids

Abstract

We compute the Rabinowitz Floer homology for a class of noncompact hyperboloids Σ ≃ S n+k−1 × R n−k . Using an embedding of a compact sphere Σ0 ≃ S 2k−1 into the hypersurface Σ, we construct a chain map from the Floer complex of Σ to the Floer complex of Σ0. In contrast to the compact case, the Rabinowitz Floer homology groups of Σ are both non-zero and not equal to its singular homology. As a consequence, we deduce that the Weinstein Conjecture holds for any strongly tentacular deformation of such a hyperboloid.