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

TL;DR

This paper provides an alternative proof that certain links are not smoothly slice in $S^2 imes S^2$, with potential implications for detecting exotic smooth structures on this 4-manifold.

Contribution

It offers a new proof of non-sliceness of links in $S^2 imes S^2$ and discusses applications to identifying exotic smooth structures.

Findings

Existence of links not smoothly slice in $S^2 imes S^2$

Alternative proof method for non-sliceness

Potential applications to exotic $S^2 imes S^2$ detection

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.