Conway knot
Prime knot named for John Horton Conway
From Wikipedia, the free encyclopedia
In mathematics, specifically in knot theory, the Conway knot (or Conway's knot) is a particular knot with 11 crossings, named after John Horton Conway.[1]
| Conway knot | |
|---|---|
| |
| Braid no. | 3[1] |
| Hyperbolic volume | 11.2191 |
| Conway notation | .−(3,2).2[2] |
| Thistlethwaite | 11n34 |
| Other | |
| hyperbolic, prime, slice (topological only), chiral | |
It is related by mutation to the Kinoshita–Terasaka knot,[3] with which it shares the same Jones polynomial.[4][5] Both knots also have the property of having the same Alexander polynomial and Conway polynomial as the unknot.[6]
The issue of the sliceness of the Conway knot was resolved in 2020 by Lisa Piccirillo, 50 years after Conway first proposed the knot.[6][7][8] Her proof made use of Rasmussen's s-invariant, and showed that the knot is not a smoothly slice knot, though it is topologically slice (the Kinoshita–Terasaka knot is both).[9]