Lectures on controlled Reeb dynamics

TL;DR

This paper provides an overview of Reeb dynamics, exploring their connection to topology and discussing various methods for constructing and analyzing Reeb flows, with implications for contact topology.

Contribution

It introduces new construction techniques like contact cuts and lifting group actions, enhancing tools for studying Reeb flows and their topological properties.

Findings

Discussion of traps and plugs for Reeb flows

Analysis of the Weinstein conjecture in specific contexts

Methods for constructing global surfaces of section

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.