Strong Corks: Applications and Construction

Four-dimensional topology exhibits remarkable phenomena that are quite different from those in other dimensions. Understanding exotic phenomena in dimension four is one of the central problems in the field, but much remains mysterious. Corks are fundamental objects closely related to various exotic phenomena in dimension four. In recent years, developments in Floer theory have led to increasing interest in the study of strong corks.

In this talk, I will first explain why strong corks are important, focusing on their applications to knot theory. I will then explain Floer-theoretic methods for detecting strong corks. Finally, I will present new infinite families of strong corks constructed in my work (arXiv:2601.02230) using equivariant Kirby calculus.