The Conway knot is not slice


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.


Lisa Piccirillo

University of Texas, Austin, TX

Current address:

Massachusetts Institute of Technology, Cambridge, MA