On the strong orderability of overtwisted 3-folds
  In this article we address the existence of positive loops of contactomorphisms in overtwisted contact 3-folds. We present a construction of such positive loops in the contact fibered connected sum of certain contact 3-folds along transverse knots. In particular, we obtain positive loops of contactomorphisms in overtwisted contact structures. 
Roger Casals, Francisco Presas
math.SG