Strong corks derived from the Akbulut cork

Abstract

We prove that the boundaries of the corks introduced by Auckly, Kim, Melvin, and Ruberman in [AKMR14] and by Tange in [Tan16] are strong corks. Furthermore, we prove that any nontrivial linear combination of them yields a strong cork, and we construct a larger family of strong corks that generalizes them. These results rely on the instanton-theoretic invariant introduced by Alfieri, Dai, Mallick, and Taniguchi in [ADMT23].