Slice knots and knot concordance

Arunima Ray

Published 2023-11-20Version 1

These notes were prepared to accompany a sequence of three lectures at the conference Winterbraids XI in Dijon, held in December 2021. In them, we provide an introduction to slice knots and the equivalence relation of concordance. We explain some connections between slice knots and exotic smooth structures on $\mathbb{R}^4$. We also introduce filtrations of the knot concordance groups and satellite operations.