Alexander's theorem

In mathematics Alexander's theorem states that every knot or link can be represented as a closed braid; that is, a braid in which the corresponding ends of the strings are connected in pairs.

The theorem is named after James Waddell Alexander II, who published a proof in 1923.

His theorem gives a positive answer to the question Is it always possible to transform a given knot into a closed braid?

This leads to a second fundamental question: Which closed braids represent the same knot type?

This question is addressed in Markov's theorem, which gives ‘moves’ relating any two closed braids that represent the same knot.