Talk
Semibounded cohomology
- Swiatoslaw Gal (University of Wrocław)
Abstract
In 2002 Polterovich proved that groups with distorted elements do not act on symplectically hyperbolic manifolds by Hamiltonian diffeomorphisms. In 2011 Jarek Kędra and the speaker simplified the proof using boundedness property of a certain cohomology class on the group of Hamiltonian diffeomorphisms. It took us about another ten years to reformulate Pollterovich theorem.
The group of Hamiltonian diffeomorphisms of a symplectically hyperbolic manifold carries a metric which respect to all elements are undistorted.
In the talk I will explain this boundedness property and discuss various situation it is useful.
