Conway knot emblem on a closed gate atIsaac Newton Institute Conway knot Prime knot named for John Horton Conway
Inmathematics , specifically inknot theory , theConway knot (orConway's knot ) is a particularknot with 11 crossings, named afterJohn Horton Conway .[ 1]
It is related bymutation to theKinoshita–Terasaka knot ,[ 3] Jones polynomial .[ 4] [ 5] Alexander polynomial andConway polynomial as theunknot .[ 6]
The issue of thesliceness of the Conway knot was resolved in 2020 byLisa Piccirillo , 50 years after John Horton Conway first proposed the knot.[ 6] [ 7] [ 8] 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]
^a b Weisstein, Eric W."Conway's Knot" .mathworld.wolfram.com . Retrieved2020-05-19 . ^ Riley, Robert (1971)."Homomorphisms of Knot Groups on Finite Groups" .Mathematics of Computation .25 (115):603– 619.doi :10.1090/S0025-5718-1971-0295332-4 ^ Chmutov, Sergei (2007)."Mutant Knots" (PDF) .Archived (PDF) from the original on 2016-12-16. ^ Kauffman, Louis H."KNOTS" .homepages.math.uic.edu . Retrieved2020-06-09 . ^ Litjens, Bart (August 16, 2011)."Knot theory and the Alexander polynomial" (PDF) .esc.fnwi.uva.nl . p. 12.Archived (PDF) from the original on 2020-06-09. Retrieved2020-06-09 . ^a b Piccirillo, Lisa (2020). "The Conway knot is not slice".Annals of Mathematics .191 (2):581– 591.doi :10.4007/annals.2020.191.2.5 .JSTOR 10.4007/annals.2020.191.2.5 . ^ Wolfson, John."A math problem stumped experts for 50 years. This grad student from Maine solved it in days" .Boston Globe Magazine . Retrieved2020-08-24 . ^ Klarreich, Erica."Graduate Student Solves Decades-Old Conway Knot Problem" .Quanta Magazine . Retrieved2020-05-19 . ^ Klarreich, Erica."In a Single Measure, Invariants Capture the Essence of Math Objects" .Quanta Magazine . Retrieved2020-06-08 .
