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 Spin(c) 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. (C) 2017 Elsevier B.V. All rights reserved.