Bott‐integrable Reeb flows on 3‐manifolds

DOI10.1112/jlms.12859arXiv2302.07701OpenAlexW4390842419MaRDI QIDQ6199338

Hansjörg Geiges, Murat Sağlam, Jakob Hedicke

Publication date: 23 February 2024

Published in: Journal of the London Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2302.07701

Mathematics Subject Classification ID

Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Global theory of symplectic and contact manifolds (53D35) Contact systems (37J55) Contact structures in 3 dimensions (57K33)

Cites Work

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• Completely integrable contact Hamiltonian systems and toric contact structures on \(S^{2}\times S^{3}\)
• Contact flows and integrable systems
• Cylindrical contact homology and topological entropy
• Contact complete integrability
• A Boothby-Wang theorem for Besse contact manifolds
• Explicit horizontal open books on some Seifert fibered 3-manifolds
• Topologically trivial Legendrian knots
• Anosov flows on new three manifolds
• The Gromov invariant of links
• Contact surgery and symplectic handlebodies
• Convexité en topologie de contact. (Convexity in contact topology)
• Contact 3-manifolds twenty years since J. Martinet's work
• Structures de contact sur les fibrés principaux en cercles de dimension trois
• Handlebody construction of Stein surfaces
• An infinity of tight contact structures on an infinity of manifolds
• On the topology of manifolds with completely integrable geodesic flows. II
• The classification of tight contact structures on the 3-torus
• On the classification of tight contact structures. II.
• Positive topological entropy for Reeb flows on 3-dimensional Anosov contact manifolds
• Seifert fibrations of lens spaces
• Reeb dynamics inspired by Katok's example in Finsler geometry
• Classification of overtwisted contact structures on 3-manifolds
• Lagrangian intersections in contact geometry
• Seifert invariants of left-quotients of 3-dimensional simple Lie groups
• Noncommutative integrability and action-angle variables in contact geometry
• Contact Anosov flows on hyperbolic 3-manifolds
• Orbit growth of contact structures after surgery
• What does a vector field know about volume?
• The topology of Bott integrable fluids
• Correction to: ``Seifert fibrations of lens spaces
• Dynamically exotic contact spheres in dimensions \(\geq 7\)
• Contact toric manifolds
• Integrable systems and group actions
• Eine Klasse von 3-dimensionalen Mannigfaltigkeiten. I, II
• Equivariant differential topology
• Surgery diagrams and open book decomposisions of contact 3-manifolds
• Reeb flows without simple global surfaces of section
• Positive topological entropy of Reeb flows on spherizations
• Contact Hamiltonian systems and complete integrability
• EXPLICIT HORIZONTAL OPEN BOOKS ON SOME PLUMBINGS
• THE TOPOLOGY OF INTEGRAL SUBMANIFOLDS OF COMPLETELY INTEGRABLE HAMILTONIAN SYSTEMS
• Entropy and Completely Integrable Hamiltonian Systems
• On the Existence of Contact Forms
• Quadrics and complete integrability in contact geometry
• ON THE DEGREE OF RATIONAL APPROXIMATION OF MEROMORPHIC FUNCTIONS
• An Introduction to Contact Topology
• The support of global graph links
• Contact structures on manifolds fibered by circles above a surface
• A symplectic dynamics proof of the degree-genus formula