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arXiv · 2606.13372

Filtered Symplectic Homology and Closed Reeb Orbits

Erman Cineli·Viktor L. Ginzburg·Basak Z. Gurel
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Abstract

We further explore connections between the symplectic homology persistence module and the properties of closed Reeb orbits for star-shaped domains in higher dimensions. Our first result is that the sequence of $S^1$-equivariant spectral invariants over a field of positive characteristic is bounded from above, in contrast with the case of characteristic zero. We also prove that the dimension of the filtered symplectic homology is bounded as a function of the action whenever the flow is a pseudo-rotation, i.e., it has finitely many prime closed orbits. Finally, we show that a non-degenerate Reeb flow has infinitely many prime closed orbits whenever it has one closed orbit with negative mean index.

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Erman Cineli, Viktor L. Ginzburg, Basak Z. Gurel. 2026-06-11. Filtered Symplectic Homology and Closed Reeb Orbits. https://arxiv.org/abs/2606.13372

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