In 2000 Eliashberg-Polterovich introduced the notion of positive contact isotopies and studied induced biinvariant partial orders on contactomorphism groups. In 2006 Eliashberg-Kim-Polterovich discovered a link to contact (non-)squeezing. At the core of these works are so-called (contractible) positive loops of contactomorphisms. Existence of or obstructions to (contractible) positive loops are difficult questions. In my talk I will explain basic notions and give simple examples illustrating these. Towards the I will explain some results concerning obstructions and a link to the famous Weinstein conjecture.
Links:
[1] http://www.mpim-bonn.mpg.de/taxonomy/term/39
[2] http://www.mpim-bonn.mpg.de/node/3444
[3] http://www.mpim-bonn.mpg.de/node/5669