Bott-integrable contact forms with large systolic ratio
Symplectic Geometry
2026-04-22 v1 Dynamical Systems
Abstract
We show that there is no universal upper bound for the systolic ratio of Bott-integrable contact forms on closed 3-manifolds, thus providing further evidence for the relative flexibility of integrable contact forms. For the proof, we study piecewise linear approximations of Lutz forms and establish integrability of a `plug' constructed by Abbondandolo, Bramham, Hryniewicz and Salom\~ao for pushing up the systolic ratio.
Keywords
Cite
@article{arxiv.2604.19237,
title = {Bott-integrable contact forms with large systolic ratio},
author = {Hansjörg Geiges and Jakob Hedicke and Murat Sağlam},
journal= {arXiv preprint arXiv:2604.19237},
year = {2026}
}
Comments
10 pages, 3 figures