Reeb Dynamics and Topological Decompositions
Joan Licata
(ANU)
Abstract
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.