Strong corks derived from the Akbulut cork

TL;DR

This paper proves that certain corks in 4-manifold topology are strong corks, introduces a larger family of such corks, and relies on instanton invariants to establish their properties.

Contribution

It demonstrates that specific known corks are strong corks and constructs a broader family of strong corks using instanton invariants.

Findings

Boundaries of corks are strong corks.

Linear combinations of these corks are also strong corks.

A larger family of strong corks is constructed.

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].