Contact structures with distinct Heegaard floer invariants

We use the Heegaard Floer theory developed by P. Ozsváth and Z. Szabó to give a new proof of a theorem of P. Lisca and G. Matić. In particular, we prove that the contact structures on Y = ∂X induced by non-homotopic Stein structures on the 4-manifold X have distinct Heegaard Floer invariants. Our examples also show that Heegaard Floer homology can distinguish between non-isotopic tight contact structures.