knot theory In the mathematical field of topology, knot theory is the study of knot (mathematics), mathematical knots. While inspired by knots which appear in daily life, such as those in shoelaces and rope, a mathematical knot differs in that the ends are ...

, the Kinoshita–Terasaka knot is a particular

prime knot In knot theory, a prime knot or prime link is a knot that is, in a certain sense, indecomposable. Specifically, it is a non-trivial knot which cannot be written as the knot sum of two non-trivial knots. Knots that are not prime are said to be co ...

. It has 11 crossings. The Kinoshita–Terasaka knot has a variety of interesting mathematical properties. It is related by

mutation In biology, a mutation is an alteration in the nucleic acid sequence of the genome of an organism, virus, or extrachromosomal DNA. Viral genomes contain either DNA or RNA. Mutations result from errors during DNA or viral replication, mi ...

to the

Conway knot 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. It is related by mutation to the Kinoshita–Terasaka knot, with which it shares the same ...

, with which it shares a

Jones polynomial In the mathematical field of knot theory, the Jones polynomial is a knot polynomial discovered by Vaughan Jones in 1984. Specifically, it is an invariant of an oriented knot or link which assigns to each oriented knot or link a Laurent polynom ...

. It has the same

Alexander polynomial In mathematics, the Alexander polynomial is a knot invariant which assigns a polynomial with integer coefficients to each knot type. James Waddell Alexander II discovered this, the first knot polynomial, in 1923. In 1969, John Conway showed a ve ...

as the

unknot In the mathematical theory of knots, the unknot, not knot, or trivial knot, is the least knotted of all knots. Intuitively, the unknot is a closed loop of rope without a knot tied into it, unknotted. To a knot theorist, an unknot is any embe ...

References

External links

K11n42 at Knot Atlas
{{DEFAULTSORT:Kinoshita-Terasaka knot Prime knots and links