When you make a link, you can use as many pieces of rope as you like, adding a new knot to the link each time you add another piece of rope.
In order to turn a link into two or more separate (un-linked) knots, you have to cut the rope. The number of times you would have to cut the rope to do this is called the link number. The link number can be thought of as a measure of how "linked up" the knots are.
When a braid is built from a series of components, the way that the ends are joined determines whether the resulting braid is a knot or a link. What determines the link number?
Every knot is a closed circular braid. Is every link a nice orderly pile of closed circular braids?
