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KNOTS AND BRAIDS

In this paper we examine two physically-inspired objects, knots and braids. The two are intimately related because when we connect the ends of a braid, we end up with a knot or link. We show that braids can be defined algebraically, geometrically, and topologically, and we determine when two braids will yield the same knot. Finally, we prove that every knot or link is the closure of some braid.