InfoIn topology, a branch of mathematics, braid theory is an abstract geometric theory studying the everyday braid concept, and some generalizations.more...The idea is that braids can be organized into groups, in which the group operation is 'do the first braid on a set of strings, and then follow it with a second on the twisted strings'. Such groups may be described by explicit presentations, as was shown by, For an elementary treatment along these lines, see the article on braid groups. Braid groups may also be given a deeper mathematical interpretation: as the fundamental group of certain configuration spaces.

Additionally, the "braid length" is the longest dimension of a braid.Braid theory has recently been applied to fluid mechanics, specifically to the field of chaotic mixing in fluid flows.…

To put the above informal discussion of braid groups on firm ground, one needs to use the homotopy concept of algebraic topology, defining braid groups as fundamental groups of a configuration space.This is outlined in the article on braid theory.Alternatively, one can define the braid group purely algebraically via the braid relations, keeping the pictures in mind only to guide the intuition.…

Braid theory is an abstract geometric theory studying the everyday braid concept, and some generalizations.The idea is that braids can be organized into groups, in which the group operation is 'do the first braid on a set of strings, and then follow it with a second on the twisted strings'.…

It is hoped that they can be used to make a quantum computer resistant to decoherence.Since the world lines form a mathematical braid, braid theory, a related field to knot theory, is used in studying the properties of such a computer, called a topological quantum computer.…

Alexander's theorem in braid theory states that the converse is true as well: every knot and every link arises in this fashion from at least one braid; such a braid can be obtained by cutting the link.Since braids can be concretely given as words in the generators, this is often the preferred method of entering knots into computer programs.…

The essential point is that one braid can wind around the other one, an operation that can be performed infinitely often, and clockwise as well as counterclockwise.A very different approach to the stability-decoherence problem in quantum computing is to create a topological quantum computer with anyons, quasi-particles used as threads and relying on braid theory to form stable logic gates.…

If M is connected, it is called a knot.While (1-dimensional) links are defined as embeddings of circles, it is often interesting and especially technically useful to consider embedded intervals (strands), as in braid theory.…

Joan Sylvia Lyttle Birman (May 30, 1927) is an American mathematician, specializing in braid theory and knot theory.Her book Braids, Links, and Mapping Class Groups has become a standard introduction, with many of today's researchers having learned the subject through it.…