On the knot types of periodic Reeb orbits of dynamically convex contact forms
Symplectic Geometry
2025-12-19 v2
Abstract
We exhibit transverse knot types on the standard contact -sphere that cannot be realized as periodic Reeb orbits of a dynamically convex contact form. In particular, such transverse knot types do not arise as closed characteristics of strictly convex energy levels on a four dimensional symplectic vector space.
Keywords
Cite
@article{arxiv.2512.08190,
title = {On the knot types of periodic Reeb orbits of dynamically convex contact forms},
author = {Umberto L. Hryniewicz and Pedro A. S. Salomão and Richard Siefring},
journal= {arXiv preprint arXiv:2512.08190},
year = {2025}
}
Comments
31 pages, with corrections and updated references. We thank Shah Faisal for spotting a mistake in the statement Theorem 1.4 of a previous version of this paper: the periodic orbit claimed to exist in the concave end is not necessarily contractible