Conway knot
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]
It is related by mutation to the Kinoshita–Terasaka knot,[2] with which it shares the same Jones polynomial.[3][4] Both knots also have the curious property of having the same Alexander polynomial and Conway polynomial as the unknot.[5]
The issue of the sliceness of the Conway knot was resolved in 2020 by Lisa Piccirillo, 50 years after John Horton Conway first proposed the knot.[5][6][7] 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).[8]
References
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External links
- Conway knot on The Knot Atlas.
- Conway knot Template:Webarchive illustrated by knotilus Template:Webarchive.