Controlled Reeb dynamics -- three lectures not in Cala Gonone

DOI10.1515/coma-2019-0006zbMath1450.37059OpenAlexW2926345048MaRDI QIDQ2311391

Hansjörg Geiges

Publication date: 10 July 2019

Published in: Complex Manifolds (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1515/coma-2019-0006

zbMATH Keywords

contact manifoldReeb dynamicscontact topologycontact cuttraps and plugs

Mathematics Subject Classification ID

Global theory of symplectic and contact manifolds (53D35) Contact manifolds (general theory) (53D10) Almost contact and almost symplectic manifolds (53D15) Contact systems (37J55) General theory of finite-dimensional Hamiltonian and Lagrangian systems, Hamiltonian and Lagrangian structures, symmetries, invariants (37J06) Relations of finite-dimensional Hamiltonian and Lagrangian systems with topology, geometry and differential geometry (symplectic geometry, Poisson geometry, etc.) (37J39)

Related Items

Closed orbits of Reeb fields on Sasakian manifolds and elliptic curves on Vaisman manifolds, Pseudorotations of the -disc and Reeb flows on the -sphere

Cites Work

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• From a Reeb orbit trap to a Hamiltonian plug
• Trapped Reeb orbits do not imply periodic ones
• Controlled constructions of Reeb fields and applications
• Examples of simply-connected symplectic non-Kählerian manifolds
• Periodic solutions of Hamiltonian system on a prescribed energy surface
• Contact 3-manifolds twenty years since J. Martinet's work
• Counterexamples to the Seifert conjecture and opening closed leaves of foliations
• On the hypotheses of Rabinowitz' periodic orbit theorems
• The dynamics on three-dimensional strictly convex energy surfaces
• Pseudoholomorphic curves in symplectizations with applications to the Weinstein conjecture in dimension three
• A Hamiltonian characterization of the three-ball
• Finite energy foliations of tight three-spheres and Hamiltonian dynamics
• A \(C^2\)-smooth counterexample to the Hamiltonian Seifert conjecture in \(\mathbb R^4\)
• Finsler geodesics, periodic Reeb orbits, and open books
• Sharp systolic inequalities for Reeb flows on the three-sphere
• Reeb dynamics inspired by Katok's example in Finsler geometry
• Classification of overtwisted contact structures on 3-manifolds
• A smooth counterexample to the Seifert conjecture
• New smooth counterexamples to the Hamiltonian Seifert conjecture.
• Topology and closed characteristics of \(K\)-contact manifolds
• Symplectic cuts
• A volume-preserving counterexample to the Seifert conjecture
• A Poincaré-Birkhoff theorem for tight Reeb flows on \(S^3\)
• Torsion contact forms in three dimensions have two or infinitely many Reeb orbits
• The Seiberg-Witten equations and the Weinstein conjecture
• On the minimal sets of non-singular vector fields
• LIFTS OF SMOOTH GROUP ACTIONS TO LINE BUNDLES
• Symplectic cobordisms and the strong Weinstein conjecture
• The Geometry of Celestial Mechanics
• On 𝐾-contact manifolds with minimal number of closed characteristics
• A smooth counterexample to the Hamiltonian Seifert conjecture in R^6
• Corrigenda to: Introduction to Symplectic Topology
• GLOBAL SURFACES OF SECTION FOR REEB FLOWS IN DIMENSION THREE AND BEYOND
• Slow volume growth for Reeb flows on spherizations and contact Bott–Samelson theorems
• Morse theory, closed geodesics, and the homology of free loop spaces
• Constructions in elliptic dynamics
• An Introduction to Contact Topology
• A formula for the Chern classes of symplectic blow-ups
• How to recognise a 4-ball when you see one
• Closed Integral Curves in 3-Space and Isotopic Two-Dimensional Deformations
• Riemannian geometry of contact and symplectic manifolds
• Contact cuts
• From one Reeb orbit to two