Tight Planar Contact Manifolds with Vanishing Heegaard Floer Contact   Invariants
  In this note, we exhibit infinite families of tight non-fillable contact manifolds supported by planar open books with vanishing Heegaard Floer contact invariants. Moreover, we also exhibit an infinite such family where the supported manifold is hyperbolic. 
James Conway, Amey Kaloti, Dheeraj Kulkarni
math.GT