Infinite order corks

Abstract

We construct a compact, contractible 4–manifold $C$, an infinite order self-diffeomorphism $f$ of its boundary, and a smooth embedding of $C$ into a closed, simply connected 4–manifold $X$, such that the manifolds obtained by cutting $C$ out of $X$ and regluing it by powers of $f$ are all pairwise nondiffeomorphic. The manifold $C$ can be chosen from among infinitely many homeomorphism types, all obtained by attaching a 2–handle to the meridian of a thickened knot complement.