New curiosities in the menagerie of corks
Kyle Hayden, Lisa Piccirillo

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 together with a self-diffeomorphism of the boundary 3-manifold that cannot extend to a self-diffeomorphism of ; the cork is said to be strong if cannot extend to a self-diffeomorphism of any smooth integer homology ball bounded by . 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 can be taken to be orientation-reversing.
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