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It is known that every compact Stein 4-manifolds can be embedded into asimply connected, minimal, closed, symplectic 4-manifold. By using thisproperty, we discuss a new method of constructing corks. This method generatesa large class of new corks including all the previously known ones. We provethat every one of these corks can knot infinitely many different ways in aclosed smooth manifold, by showing that cork twisting along them givesdifferent exotic smooth structures. We also give an example of infinitely manydisjoint embeddings of a fixed cork into a non-compact 4-manifold which produceinfinitely many exotic smooth structures. Furthermore, we construct arbitrarymany simply connected compact codimension zero submanifolds of S^4 which aremutually homeomorphic but not diffeomorphic.

Stein 4-manifolds and corks