Infinite order corks

Robert E. Gompf

Published 2016-03-16Version 1

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, revealing a new construction of corks: attaching a 2-handle to the meridian of a thickened knot complement.