Strongly invertible Whitehead doubles and involutive Heegaard Floer homology

Two smoothly embedded surfaces in a smooth 4-manifold are called exotic if they are topologically isotopic but not smoothly isotopic. The phenomenon of exotic surfaces in dimension 4 is an interesting topic in low-dimensional topology. In this talk, we start with an introduction to equivariant knot concordance theory in the context of exotic disks. Then we recall how involutive Heegaard Floer theory can work as a machinery for equivariant concordance. Then we demonstrate our recent progress on equivariant concordance of Whitehead doubles, which produces exotic disk pairs.

This is joint work with Sungkyung Kang and JungHwan Park.