Infinite order corks

TL;DR

This paper constructs a special 4-manifold with an infinite-order boundary diffeomorphism, demonstrating how regluing it produces infinitely many non-diffeomorphic smooth structures on a closed 4-manifold.

Contribution

It introduces a new infinite-order cork construction that generates infinitely many exotic smooth structures via boundary regluing.

Findings

Constructed a compact, contractible 4-manifold with an infinite-order boundary diffeomorphism.

Demonstrated that regluing by powers of this diffeomorphism yields infinitely many nondiffeomorphic manifolds.

Provided explicit examples from handle attachments to knot complements.

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.