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arXiv · 2006.16839

Computing the Rabinowitz Floer homology of tentacular hyperboloids

Alexander Fauck·Will J. Merry·Jagna Wiśniewska
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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.

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Alexander Fauck, Will J. Merry, Jagna Wiśniewska. 2020-06-30. Computing the Rabinowitz Floer homology of tentacular hyperboloids. https://doi.org/10.3934/jmd.2021013

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