Computing the Rabinowitz Floer homology of tentacular hyperboloids

Abstract

We compute the Rabinowitz Floer homology for a class of non-compact hyperboloids $\Sigma \simeq S^{n+k-1}\times {\mathbb{R}}^{n-k}$. Using an embedding of a compact sphere ${\Sigma }_0\simeq S^{2k-1}$ into the hypersurface $\Sigma$, we construct a chain map from the Floer complex of $\Sigma$ to the Floer complex of ${\Sigma }_0$. In contrast to the compact case, the Rabinowitz Floer homology groups of $\Sigma$ 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.

v2: Fixed eleven typos in the title

References in corpus (4)

• Covariantly functorial wrapped Floer theory on Liouville sectors
• Rabinowitz Floer homology and mirror symmetry
• Contact orderability up to conjugation
• Bounds for tentacular Hamiltonians