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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.
The composition of the braids σ and τ is written as στ.. The set of all braids on four strands is denoted by .The above composition of braids is indeed a group operation. . The identity element is the braid consisting of four parallel horizontal strands, and the inverse of a braid consists of that braid which "undoes" whatever the first braid did, which is obtained by flipping a diagram ...
Box braids in Ethiopia American singer/actress Brandy Norwood with her signature [1] box braids. 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 ...
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.
Spin representations can be analysed according to the following strategy: if S is a real spin representation of Spin(p, q), then its complexification is a complex spin representation of Spin(p, q); as a representation of so(p, q), it therefore extends to a complex representation of so(n, C).
Spin network diagram, after Penrose. In physics, a spin network is a type of diagram which can be used to represent states and interactions between particles and fields in quantum mechanics. From a mathematical perspective, the diagrams are a concise way to represent multilinear functions and functions between representations of matrix groups ...
The diagram algebra for () is deduced from the diagram algebra for () by turning rectangles into cylinders. The algebra a T L n ( δ ) {\displaystyle aTL_{n}(\delta )} is infinite-dimensional because lines can wind around the cylinder.
In mathematics and theoretical physics, braid statistics is a generalization of the spin statistics of bosons and fermions based on the concept of braid group.While for fermions (bosons) the corresponding statistics is associated to a phase gain of () under the exchange of identical particles, a particle with braid statistics leads to a rational fraction of under such exchange [1] [2] or even ...