On contact type hypersurfaces in 4-space

We consider constraints on the topology of closed 3-manifolds that can arise as hypersurfaces contact type in standard symplectic $R^4$. Using an obstruction derived from Heegaard Floer homology we prove no Brieskorn sphere admits a embedding $R^4$, result has bearing conjectures Gompf and Koll\'ar. This implies particular rationally convex domain $C^2$ boundary diffeomorphic to sphere. also give infinitely many examples bound Stein domains but not symplectically ones; find cannot be made Weinstein with respect ambient structure while preserving their boundaries.