Brunnian link information

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...

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...

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...

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...

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...

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

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 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...

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 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....

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...

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)...

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...

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...

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...

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

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...

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...

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...

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

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...

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

\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...

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

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...