Knot diagrams and twisted plats

Jessica Purcell (BYU)

Abstract: Certain diagrams of knots allow you to read off geometric and topological information more easily than others. One such diagram is a highly twisted plat projection. Every knot has a plat projection; if the diagram also happens to have at least three crossings in each twist region, we say it is highly twisted. In this talk, we will discuss highly twisted plat projections and the geometric and topological facts we know about such knots from a diagram. We show that if a knot admits a highly twisted plat projection, then it admits a unique such diagram. This is joint work with Yoav Moriah.