Chris Wendl (Humboldt Universitat, Berlin): A Hierarchy of Filling Obstructions for Contact Manifolds

It is a standard fact that overtwisted contact 3-manifolds are not symplectically fillable, and more recent results show that there are also many tight but non-fillable contact manifolds, namely those which have Giroux torsion. I will explain how these two obstructions can be understood as the first two levels in an infinite hierarchy of filling obstructions, collectively called planar torsion, which can be used to find contact manifolds that are not strongly or weakly fillable but have no Giroux torsion. The proof uses pseudoholomorphic curves.