Filtered Symplectic Homology and Closed Reeb Orbits

2026/06/11 by Erman Cineli, Viktor L. Ginzburg, Basak Z. Gurel · 1 voice
Mathematics · #math.SG #math.DS

paper · pdf

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 S¹-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.

Citations

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Discussions

• Erman Cineli, Viktor L. Ginzburg, Basak Z. Gurel: Filtered Symplectic Homology and Closed Reeb Orbits https://arxiv.org/abs/2606.13372 https://arxiv.org/pdf/2606.13372 https://arxiv.org/html/2606.1337 [bsky, 0 points, 0 comments]

Related

• On the Filtered Symplectic Homology of Prequantization Bundles
• Local Symplectic Homology of Reeb Orbits
• Multiplicity of closed Reeb orbits on contact manifolds with periodic equivariant symplectic homology
• On the growth rate of Reeb orbit on star-shaped hypersurfaces
• Closed Orbits of Dynamically Convex Reeb Flows: Towards the HZ- and Multiplicity Conjectures