Positive loops---on a question by Eliashberg-Polterovich and a contact systolic inequality

Princeton/IAS Symplectic Geometry Seminar
Topic:Positive loops---on a question by Eliashberg-Polterovich and a contact systolic inequality
Speaker:Peter Albers
Affiliation:Universit√§t M√ľnster
Date:Thursday, February 25
Time/Room:10:30am - 11:45am/S-101
Video Link:https://video.ias.edu/puias/2016/0225-Albers

In 2000 Eliashberg-Polterovich introduced the concept of positivity in contact geometry. The notion of a positive loop of contactomorphisms is central. A question of Eliashberg-Polterovich is whether $C^0$-small positive loops exist. We give a negative answer to this question. Moreover we give sharp lower bounds for the size which, in turn, gives rise to a $L^\infty$-contact systolic inequality. This should be contrasted with a recent result by Abbondandolo et. al. that on the standard contact 3-sphere no $L^2$-contact systolic inequality exists. The choice of $L^2$ is motivated by systolic inequalities in Riemannian geometry. This is joint work with U. Fuchs and W. Merry.