Conway knot

Conway knot
Braid no.3[1]
Hyperbolic volume11.2191
Conway notation.−(3,2).2[2]
Thistlethwaite11n34
Other
hyperbolic, prime, slice (topological only), chiral
Conway knot emblem on a closed gate at Isaac Newton Institute
Conway knot
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,[3] with which it shares the same Jones polynomial.[4][5] Both knots also have the curious 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 John Horton 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]

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