A braid is an intertwining of some number of strings attached to top and bottom "bars" such that each string never "turns back up." In other words, the path of
each string in a braid could be traced out by a falling object if acted upon only
by gravity and horizontal forces. A given braid may be assigned a symbol known as
a braid word that uniquely identifies it (although
equivalent braids may have more than one possible representations). For example,
is a braid word for the braid illustrated above.
If 
is a knot and
where 
is the Alexander
polynomial of 
,
then 
cannot be represented
as a closed 3-braid. Also, if
then 
cannot be represented
as a closed 4-braid (Jones 1985).
See also
Braid Group, Braid Index, Braid Word, Knot, Link
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References
Artin, E. "The Theory of Braids." Amer. Sci. 38, 112-119, 1950.
Christy, J. "Braids." http://library.wolfram.com/infocenter/MathSource/813/.Jones,
V. "A Polynomial Invariant for Knots via von Neumann Algebras." Bull.
Amer. Math. Soc. 12, 103-111, 1985.Murasugi, K. and Kurpita,
B. I. A
Study of Braids. Dordrecht, Netherlands: Kluwer, 1999.
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Cite this as:
Weisstein, Eric W. "Braid." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/Braid.html