New curiosities in the menagerie of corks

TL;DR

This paper introduces the first examples of non-strong corks and corks with orientation-reversing boundary diffeomorphisms, expanding the understanding of exotic smooth structures in 4-manifold topology.

Contribution

It constructs the first non-strong corks and corks with orientation-reversing boundary maps, providing new examples of exotic Mazur manifolds.

Findings

First non-strong corks constructed

Examples of corks with orientation-reversing boundary diffeomorphisms

New exotic Mazur manifolds introduced

Abstract

A cork is a smooth, contractible, oriented, compact 4-manifold $W$ together with a self-diffeomorphism $f$ of the boundary 3-manifold that cannot extend to a self-diffeomorphism of $W$; the cork is said to be strong if $f$ cannot extend to a self-diffeomorphism of any smooth integer homology ball bounded by $\partial W$. Surprising recent work of Dai, Hedden, and Mallick showed that most of the well-known corks in the literature are strong. We construct the first non-strong corks, which also give rise to new examples of absolutely exotic Mazur manifolds. Additionally we give the first examples of corks where the diffeomorphism of $\partial W$ can be taken to be orientation-reversing.