# The Conway knot is not slice

### Abstract

A knot is said to be slice if it bounds a smooth properly embedded disk in $B^4$. We demonstrate that the Conway knot is not slice. This completes the classification of slice knots under 13 crossings and gives the first example of a non-slice knot which is both topologically slice and a positive mutant of a slice knot.

## Authors

Lisa Piccirillo

University of Texas, Austin, TX