A note on smoothly slice links in $S^2 \times S^2$

Abstract

We give an alternative proof of a result of Miyazaki and Yasuhara that there exists links that are not smoothly slice in $S^2 \times S^2$. We discuss potential applications to the detection of exotic $S^2 \times S^2$. This is a follow-up note to a similar paper for the $\mathbb{CP}^2 \# \overline{\mathbb{CP}^2}$ case.