---
tag: P68G28E4AD
kind: concept
name: Slice knot
msc: [57K10, 57K40]
specializes: [QYEAZTYGPT]
sources:
  - url: https://en.wikipedia.org/wiki/Slice_knot
same_as:
  wikidata: Q7540228
  wikipedia: Slice knot
---

## Summary

A slice knot is a [[knot|QYEAZTYGPT]] in the $3$-sphere that bounds a smoothly embedded disk in the $4$-ball.
The notion links knot theory with the topology of [[4-manifolds|8H58Q6YJCH]].
Slice knots are exactly the knots concordant to the [[unknot|1TQ06R4Q66]], and they form the zero element of the knot concordance group.
There is also a topological version, with locally flat disks, and the two versions differ.

## Explanations

### L1 human

View ordinary space as the boundary of a four-dimensional ball, as a circle is the boundary of a disk.
A knot is slice if, with the help of the extra dimension, it bounds a disk without self-intersections.
In three dimensions only the unknot bounds such a disk, but in four dimensions many knots do.
The sum of a knot and its reversed mirror image is always slice.
The [[trefoil knot|VYTYSVHN4A]] is not slice.