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...

the Borromean rings can be proved to be linked by counting their Fox n-colorings. As links, they are Brunnian, alternating, algebraic, and hyperbolic...

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...

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...

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...

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...

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...

the linking number is a numerical invariant that describes the linking of two closed curves in three-dimensional space. Intuitively, the linking number...

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...

in convex geometry (see Brunn–Minkowski inequality) and in knot theory. Brunnian links are named after him, as his 1892 article "Über Verkettung" included...

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....

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...

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)...

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...

of interest because it is presumably the simplest link which possesses the Brunnian property — a link of connected components that, when one component...

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...

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...

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...

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...

Brunnian Chirality Invertible Crosscap no. Crossing no. Finite type invariant Hyperbolic volume Khovanov homology Genus Knot group Link group Linking...

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...

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...

needed to realize a particular knot type. Linking number – Numerical invariant that describes the linking of two closed curves in three-dimensional space...

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...

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...

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...

Brunnian Chirality Invertible Crosscap no. Crossing no. Finite type invariant Hyperbolic volume Khovanov homology Genus Knot group Link group Linking...

\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...

area of knot theory, a Reidemeister move is any of three local moves on a link diagram. Kurt Reidemeister (1927) and, independently, James Waddell Alexander...

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...