Mathematics Colloquium - Tye Lidman
Usually, when we draw a knotted loop in space, we draw a projection to the plane and study the over and under crossings. It is natural to ask how structural properties of the knot are reflected in the diagrammatics. For example, which of the crossings are “topologically intrinsic” to the knot, and how does changing one crossing from over to under alter the knot? We will discuss how to extract this information using the topology of the three-manifolds.