Planar Lefschetz fibrations and Stein structures with distinct   Ozsvath-Szabo invariants on corks
  Thanks to a result of Lisca and Matic and a refinement by Plamenevskaya, it is known that on a 4-manifold with boundary Stein structures with non-isomorphic Spinc structures induce contact structures with distinct Ozsvath-Szabo invariants. Here we give an infinite family of examples showing that converse of Lisca-Matic-Plamenevskaya theorem does not hold in general. Our examples arise from Mazur type corks. 
Cagri Karakurt, Takahiro Oba, Takuya Ukida
math.GT math.SG