English

The Conway knot is not slice

Geometric Topology 2018-08-10 v1

Abstract

A knot is said to be slice if it bounds a smooth properly embedded disk in the 4-ball. We demonstrate that the Conway knot, 11n34 in the Rolfsen tables, 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.

Keywords

Cite

@article{arxiv.1808.02923,
  title  = {The Conway knot is not slice},
  author = {Lisa Piccirillo},
  journal= {arXiv preprint arXiv:1808.02923},
  year   = {2018}
}

Comments

9 pages, 4 figures (one of which is large), 1 table

R2 v1 2026-06-23T03:28:17.408Z