New curiosities in the menagerie of corks

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 ∂ 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 ∂ W can be taken to be orientation-reversing.