The study of braids and their closures has been a phenomenal source of inspiration for many advances in knot theory. For instance, the current state-of -the-art algorithm for unknot recognition depends on foliation techniques that arise in the study of closed braids. Recently, work has been done on a different type of braid closure called the plat closure. This research is in its infancy, but boasts many promising advantages (and of course some disadvantages) to the study standard braid closures. Below are some introductory notes on the topic.
These notes are currently in preparation below is a working draft: