A hierarchy of local symplectic filling obstructions for contact 3-manifolds
A hierarchy of local symplectic filling obstructions for contact 3-manifolds
We generalize the familiar notions of overtwistedness and Giroux torsion in 3-dimensional contact manifolds, defining an infinite hierarchy of local filling obstructions called planar torsion, whose integer-valued order $k \ge 0$ can be interpreted as measuring a gradation in "degrees of tightness" of contact manifolds. We show in particular that …