Every knot or link has a diagram that is a plat projection. We show that if the plat is "sufficiently complicated," then the plat projection is unique. In particular, this projection gives a canonical form for such knots and links, and thus provides a classification of these links. In this talk, we will discuss this result, giving a precise statement of what we mean by sufficiently complicated, and motivating the classification problem for links via diagrams.
This is joint work with Prof. Yoav Moriah (Technion - Israel Institute of Technology).