Modul: MAT075 Zurich Graduate Colloquium

## What is... a slice knot?

Talk by Paula Truöl

**Date:** 16.11.21 **Time:** 16.30 - 17.30 **Room:**

Knot theory is a subarea of low-dimensional topology - the study of smooth manifolds of dimension 4 or less. Classical knots are smooth embeddings of the (oriented) circle S^1 into R^3 (or into the 3-sphere), usually studied up to an equivalence relation called ambient isotopy. The concept of "sliceness" is a (natural) generalization in dimension 4 of the question whether certain knots are isotopic to the trivial knot (the so-called unknot). In the talk, we will define all the relevant terms and give examples of slice knots. Along the way, we will see some related important results from low-dimensional topology. For example, the study of slice knots is connected to the existence of "exotic" smooth structures on R^4.