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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.
A size chart illustrating the ANSI sizes. In 1992, the American National Standards Institute adopted ANSI/ASME Y14.1 Decimal Inch Drawing Sheet Size and Format, [1] which defined a regular series of paper sizes based upon the de facto standard 8 + 1 ⁄ 2 in × 11 in "letter" size to which it assigned the designation "ANSI A".
A braided monoidal category is a monoidal category equipped with a braiding—that is, a commutativity constraint that satisfies axioms including the hexagon identities defined below. The term braided references the fact that the braid group plays an important role in the theory of braided monoidal categories.
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 ...
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 ...
Every non-trivial knot has bridge number at least two, [1] so the knots that minimize the bridge number (other than the unknot) are the 2-bridge knots.It can be shown that every n-bridge knot can be decomposed into two trivial n-tangles and hence 2-bridge knots are rational knots.
A navigational box that can be placed at the bottom of articles. Template parameters [Edit template data] Parameter Description Type Status State state The initial visibility of the navbox Suggested values collapsed expanded autocollapse String suggested Template transclusions Transclusion maintenance Check completeness of transclusions The above documentation is transcluded from Template ...
DuPont made public in 1938 that their company had invented nylon. [1] This new invention was the first synthetic fiber, fabrics that are commonly used in textiles today. [2] In 1939, DuPont began marketing nylon monofilament fishing lines; however, braided Dacron lines remained the most used and popular fishing line for the next two decades, as early monofilament line was very stiff or "wiry ...
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