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BRAID THEORY Martin Bendersky, Dept. of Math. & Stat. at Hunter A braid is what you might imagine it to be - a weaving of some strings between two posts. E. Artin showed how to endow an algebraic structure on the collection of all braids with n strings. The structure has some similarities with the usual multiplication laws. There is an identity (similar to 1), namely, the braid with no weaving. There are also inverses. There are dissimilarities as well. Multiplication of two braids does not commute. Artin was able to completely describe the structure (which is now called the Artin Braid Group) and provide a prime decomposition law for a special class of braids. The problem of how to tell when two braids (and a related object called a knot) are the same is one of the important fields in mathematics (specifically, algebra and topology).
