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This is a typical element of the braid group, which is used in the mathematical field of knot theory. In mathematics Alexander's theorem states that every knot or link can be represented as a closed braid ; that is, a braid in which the corresponding ends of the strings are connected in pairs.
The standard braid is Brunnian: if one removes the black strand, the blue strand is always on top of the red strand, and they are thus not braided around each other; likewise for removing other strands. A Brunnian braid is a braid that becomes trivial upon removal of any one of its strings. Brunnian braids form a subgroup of the braid group.
Box braids are a type of hair-braiding style that is predominantly popular among African people and the African diaspora. This type of hairstyle is a "protective style" (a style which can be worn for a long period of time to let natural hair grow and protect the ends of the hair) and is "boxy", consisting of square-shaped hair divisions.
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Braids, Links, and Mapping Class Groups is a mathematical monograph on braid groups and their applications in low-dimensional topology.It was written by Joan Birman, based on lecture notes by James W. Cannon, [1] and published in 1974 by the Princeton University Press and University of Tokyo Press, as volume 82 of the book series Annals of Mathematics Studies.
In knot theory, the trefoil is the first nontrivial knot, and is the only knot with crossing number three. It is a prime knot, and is listed as 3 1 in the Alexander-Briggs notation. The Dowker notation for the trefoil is 4 6 2, and the Conway notation is [3]. The trefoil can be described as the (2,3)-torus knot.
Knotless Braids: A variation of box braids, starting with natural hair and gradually adding extensions, reducing scalp tension.Knotless braids do not include the knots. Crochet braids : Extensions are crocheted into cornrowed natural hair, offering a variety of styling options.
A string link need not be a braid – it may double back on itself, such as a two-component string link that features an overhand knot. A braid that is also a string link is called a pure braid, and corresponds with the usual such notion. The key technical value of tangles and string links is that they have algebraic structure.