Reeb Dynamics and Topological Decompositions

Joan Licata


A contact form on a three-manifold determines a foliation by one-manifolds called Reeb orbits, and these are the building blocks for a family of contact invariants coming from symplectic field theory. Recent efforts to model these invariants topologically suggest the following question: given a decomposition of a three-manifold M into one-manifolds, is there a contact form on M whose Reeb orbits realize the decomposition? This talk will discuss related obstructions, necessary conditions, and open questions, as well as introducing the topological invariants which motivate the topic.

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