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 |
In mathematics, in particular 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]
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 |
In mathematics, in particular 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]