Conway knot
| Conway knot | |
|---|---|
 | |
| Crossing no. | 11 |
| Genus | 3 |
| Thistlethwaite | 11n34 |
| Other | |
| , prime | |
In mathematics, in particular 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.[citation needed]
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] Her proof made use of Rasmussen's s-invariant, and showed that the knot is not a slice knot.[7]
References
- ^ Weisstein, Eric W. "Conway's Knot". mathworld.wolfram.com. Retrieved 2020-05-19.
- ^ "Mutant Knots" (PDF). 2007.
{{cite web}}: CS1 maint: url-status (link) - ^ "KNOTS". homepages.math.uic.edu. Retrieved 2020-06-09.
- ^ Litjens, Bart (August 16, 2011). "Knot theory and the Alexander polynomial" (PDF). esc.fnwi.uva.nl. p. 12. Retrieved 9 June 2020.
{{cite web}}: CS1 maint: url-status (link) - ^ Klarreich, Erica. "Graduate Student Solves Decades-Old Conway Knot Problem". Quanta Magazine. Retrieved 2020-05-19.
- ^ 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.
- ^ Klarreich, Erica. "In a Single Measure, Invariants Capture the Essence of Math Objects". Quanta Magazine. Retrieved 2020-06-08.
External links
- Conway knot on The Knot Atlas.
- Conway knot illustrated by knotilus.
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