Bott-integrability of overtwisted contact structures

2025/01/10 by Hansjörg Geiges, Geiges, Hansjörg, Jakob Hedicke +3 · 1 voice · 1 citation
Mathematics · #37J35 #37J55 #53D35 #57K33 #Dynamical Systems (math.DS) #FOS: Mathematics #Symplectic Geometry (math.SG) #math.DS #math.SG

paper · pdf · doi:10.48550/arxiv.2501.05784

arxiv published 2025/01/10 · arxiv updated 2025/03/25

Abstract

We show that an overtwisted contact structure on a closed, oriented 3-manifold can be defined by a contact form having a Bott-integrable Reeb flow if and only if the Poincaré dual of its Euler class is represented by a graph link.

Cited by

• Bott-integrable contact forms with large systolic ratio

Discussions

• Hansj\"org Geiges, Jakob Hedicke, Murat Sa\u{g}lam: Bott-integrability of overtwisted contact structures https://arxiv.org/abs/2501.05784 https://arxiv.org/pdf/2501.05784 https://arxiv.org/html/2501.0 [bsky, 0 points, 1 comments]

Related

• A Note on Overtwisted Contact Structures
• Existence and classification of overtwisted contact structures in all dimensions
• Bott-integrable contact forms with large systolic ratio
• Links in overtwisted contact manifolds
• Tight contact structures on 3-manifolds via dynamics