Braid Closure
Braid Closure
For any braid
, its closure is the link that results from connecting the lower ends of the braid with the upper ends in the same order.
e.g. The closure of 
Alexander's Theorem
Any knot or link can be represented as a closed braid. i.e.
is surjective.
Proof
Remark
In a certain sense, braids are the quantum analog of permutations.
Markov Moves
Markov's Theorem