Alexander's Theorem guarantees that every oriented link is the closure of some braid. In other words, the map


$$ \displaystyle \coprod\\_n \mathcal B\_n\longrightarrow \{\text{ oriented links }\} $$


is surjective. One algorithm (I'm actually not sure that it's Alexander's original demonstration) involves choosing a basepoint in the complement of a diagram for the link and applying Reidemeister moves until the resulting diagram winds around the point in a consistent direction, at which point the diagram is manifestly the closure of a link.



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> If we begin with a positive diagram for a link, then do we necessarily obtain a positive braid?
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Is a positive link the closure of a positive braid?
Rudolph proved that [positive links are strongly quasipositive](http://www.ams.org/mathscinet-getitem?mr=1734423). [This paper](http://www.ams.org/mathscinet-getitem?mr=894383) might also be relevant, which allows one to create a braid with the same number of Seifert circles and writhe. However, Yamada's algorithm doesn't seem to preserve positivity either. 


