Bott-integrable contact forms with large systolic ratio

TL;DR

The paper demonstrates that Bott-integrable contact forms on closed 3-manifolds can have arbitrarily large systolic ratios, highlighting their flexibility, by analyzing piecewise linear approximations and a specialized 'plug' construction.

Contribution

It proves the absence of a universal upper bound for systolic ratios of Bott-integrable contact forms on closed 3-manifolds, using novel approximation and integrability techniques.

Findings

No universal upper bound for systolic ratio of Bott-integrable contact forms.

Piecewise linear approximations of Lutz forms are effective in the analysis.

A 'plug' construction can be used to increase systolic ratios.

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.