Controlled Reeb dynamics — Three lectures not in Cala Gonone

Abstract

These are notes based on a mini-course at the conference RIEMain in Contact, held in Cagliari, Sardinia, in June 2018. The main theme is the connection between Reeb dynamics and topology. Topics discussed include traps for Reeb flows, plugs for Hamiltonian flows, the Weinstein conjecture, Reeb flows with finite numbers of periodic orbits, and global surfaces of section for Reeb flows. The emphasis is on methods of construction, e.g. contact cuts and lifting group actions in Boothby–Wang bundles, that might be useful for other applications in contact topology.

Keywords

• contact manifold
• reeb dynamics
• traps and plugs
• contact cut
• global surface of section
• msc 2010: 37j05 (primary) 37c27
• 37j45
• 53d20
• 53d35 (secondary)