Notes on Gompf's Infinite Order Corks

For any positive integer n, we give a Z(n)-cork with a Z(n)-effective embedding in a 4-manifold being homeomorphic to E(n). This means that a cork gives a subset Z(n) in the differential structures on E(n). Further, we describe handle decompositions of the twisted doubles (homotopy S-4) of Gompf's infinite order cork and show that they are log transforms of S-4.