Search Results for ""

For a braid with M strands, R components, P positive crossings, and N negative crossings, {P-N<=U_++M-R if P>=N; P-N<=U_-+M-R if P<=N, (1) where U_+/- are the smallest number ...

Let G be a group, then there exists a piecewise linear knot K^(n-2) in S^n for n>=5 with G=pi_1(S^n-K) iff G satisfies 1. G is finitely presentable, 2. The Abelianization of ...

In the 1930s, Reidemeister first rigorously proved that knots exist which are distinct from the unknot. He did this by showing that all knot deformations can be reduced to a ...

A B-spline is a generalization of the Bézier curve. Let a vector known as the knot vector be defined T={t_0,t_1,...,t_m}, (1) where T is a nondecreasing sequence with t_i in ...

The twist of a ribbon measures how much it twists around its axis and is defined as the integral of the incremental twist around the ribbon. A formula for the twist is given ...

Vassiliev invariants, discovered around 1989, provided a radically new way of looking at knots. The notion of finite type (a.k.a. Vassiliev) knot invariants was independently ...

A 2-variable oriented knot polynomial P_L(a,z) motivated by the Jones polynomial (Freyd et al. 1985). Its name is an acronym for the last names of its co-discoverers: Hoste, ...

An object that is not superimposable on its mirror image is said to be dissymmetric. All asymmetric objects are dissymmetric, and an object with no improper rotation ...

Two nonsuperimposable objects which are mirror images of each other are called enantiomers. The term enantiomer is synonymous with enantiomorph. For example, the letters b ...

Conjugation is the process of taking a complex conjugate of a complex number, complex matrix, etc., or of performing a conjugation move on a knot. Conjugation also has a ...