In knot theory, a branch of topology, a Brunnian link is a nontrivial link that becomes a set of trivial unlinked circles if any one component is removed...
10 KB (1,141 words) - 11:25, 9 September 2024
Borromean rings (redirect from Borromean link)
the Borromean rings can be proved to be linked by counting their Fox n-colorings. As links, they are Brunnian, alternating, algebraic, and hyperbolic...
43 KB (4,472 words) - 10:49, 27 August 2024
rings are collectively linked despite the fact that no two of them are directly linked. The Borromean rings thus form a Brunnian link and in fact constitute...
8 KB (1,107 words) - 01:03, 25 April 2024
which are linked and form a Brunnian link (L6a4) L10a140 link - presumably the simplest non-Borromean Brunnian link Pretzel link - a Montesinos link with integer...
3 KB (421 words) - 23:35, 12 September 2023
Rainbow Loom (category Commons category link is on Wikidata)
pulled by a rainbow loom crochet hook. The resulting looped knots, known as Brunnian links, can be assembled on the loom into bracelets and other shapes. The...
17 KB (1,792 words) - 17:25, 25 April 2024
Unlink (redirect from Trivial Link)
there exists a hyperbolic link of n components such that any proper sublink is an unlink (a Brunnian link). The Whitehead link and Borromean rings are such...
3 KB (238 words) - 00:19, 26 March 2024
Enneagram (geometry) (category Commons category link from Wikidata)
triangles. (If the triangles are alternately interlaced, this results in a Brunnian link.) This star figure is sometimes known as the star of Goliath, after...
5 KB (367 words) - 16:27, 8 March 2024
In mathematics, a hyperbolic link is a link in the 3-sphere with complement that has a complete Riemannian metric of constant negative curvature, i.e....
2 KB (222 words) - 13:00, 27 July 2024
the simplest Brunnian link Brunnian link, a set of links which become trivial if one loop is removed Hopf link, the simplest non-trivial link Solomon's knot...
7 KB (788 words) - 23:17, 22 May 2024
the linking number is a numerical invariant that describes the linking of two closed curves in three-dimensional space. Intuitively, the linking number...
16 KB (2,527 words) - 16:29, 10 June 2024
In the mathematical theory of knots, a pretzel link is a special kind of link. It consists of a finite number of tangles made of two intertwined circular...
8 KB (1,004 words) - 23:34, 9 February 2023
in convex geometry (see Brunn–Minkowski inequality) and in knot theory. Brunnian links are named after him, as his 1892 article "Über Verkettung" included...
2 KB (134 words) - 11:26, 18 July 2024
theory, the Whitehead link, named for J. H. C. Whitehead, is one of the most basic links. It can be drawn as an alternating link with five crossings, from...
6 KB (651 words) - 18:56, 26 December 2021
mathematical knot theory, the Hopf link is the simplest nontrivial link with more than one component. It consists of two circles linked together exactly once, and...
9 KB (892 words) - 16:20, 15 November 2022
Knot theory (redirect from Link diagram)
gives the unknot and the Hopf link. Applying the relation to the Hopf link where indicated, C() = C() + z C() gives a link deformable to one with 0 crossings...
49 KB (6,295 words) - 22:27, 12 July 2024
Prime knot (redirect from Composite link)
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...
3 KB (271 words) - 16:54, 20 August 2024
order of m k + 1 / k 2 {\displaystyle m^{k+1}/k^{2}} . Link groups can be used to classify Brunnian links. Knot group Regular homotopy Cochran, Tim D. (1990)...
8 KB (1,236 words) - 19:46, 18 December 2023
of interest because it is presumably the simplest link which possesses the Brunnian property — a link of connected components that, when one component...
6 KB (1,165 words) - 18:43, 12 May 2024
Torus knot (redirect from Torus link)
link is a link which lies on the surface of a torus in the same way. Each torus knot is specified by a pair of coprime integers p and q. A torus link...
16 KB (1,790 words) - 13:16, 27 July 2024
Solomon's knot (redirect from Solomon link)
times, and found in many cultures. Despite the name, it is classified as a link, and is not a true knot according to the definitions of mathematical knot...
11 KB (1,332 words) - 06:52, 21 August 2024
In mathematics, Khovanov homology is an oriented link invariant that arises as the cohomology of a cochain complex. It may be regarded as a categorification...
11 KB (1,464 words) - 23:17, 22 May 2024
Specifically, it is an invariant of an oriented knot or link which assigns to each oriented knot or link a Laurent polynomial in the variable t 1 / 2 {\displaystyle...
17 KB (2,339 words) - 23:46, 13 August 2024
Fibered knot (redirect from Fibered link)
In knot theory, a branch of mathematics, a knot or link K {\displaystyle K} in the 3-dimensional sphere S 3 {\displaystyle S^{3}} is called fibered or...
4 KB (419 words) - 20:04, 27 August 2022
Knot complement (redirect from Knot and link complements)
is needed to determine the usage. There are analogous definitions for the link complement. Many knot invariants, such as the knot group, are really invariants...
3 KB (275 words) - 00:23, 24 October 2023
Alternating knot (redirect from Alternating link)
knot or link diagram is alternating if the crossings alternate under, over, under, over, as one travels along each component of the link. A link is alternating...
6 KB (681 words) - 03:53, 29 January 2022
Knot invariant (redirect from Link invariant)
needed to realize a particular knot type. Linking number – Numerical invariant that describes the linking of two closed curves in three-dimensional space...
10 KB (1,269 words) - 23:58, 31 January 2023
Writhe (section Writhe of link diagrams)
\operatorname {Wr} } . In one sense, it is purely a property of an oriented link diagram and assumes integer values. In another sense, it is a quantity that...
10 KB (1,465 words) - 11:50, 12 September 2024
Chiral knot (redirect from Amphichiral link)
Brunnian Chirality Invertible Crosscap no. Crossing no. Finite type invariant Hyperbolic volume Khovanov homology Genus Knot group Link group Linking...
8 KB (700 words) - 14:15, 10 July 2024
2-bridge knot (redirect from Rational link)
numbers; the rational number associated to a given link is called the Schubert normal form of the link (as this invariant was first defined by Schubert)...
3 KB (308 words) - 08:38, 15 December 2023