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.

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Authors

Lisa Piccirillo

University of Texas, Austin, TX

Current address:

Massachusetts Institute of Technology, Cambridge, MA