ABSTRACT
This chapter discusses Alexander's theorem that each link can be obtained as a braid closure. It provides two proofs of this theorem: the original one by Alexander and the one by P. Vogel that realises a faster algorithm for constructing a corresponding braid. The method of proof for Alexander's theorem gives a concrete algorithm for constructing a braid from a link. The chapter explains a simpler algorithm for constructing braids by links. Proof actually, consider the edges of this side. It is easy to see that all edges belonging to the same Seifert circle have the same orientation. A braided link diagram can be easily represented as a closure of a braid. If all Seifert circles of some planar link diagram are nested, then the corresponding diagram is braided. Moreover, in this case, the number of strands of the braid coincides with the number of Seifert circles.
