Speaker：Jim Hoste（Pitzer College，USA）

Time：2019-04-15,10:00

Location：Conference Room 105 at Experiment Building at Haiyun Campus

Abstract:The mathematical study of knots began in the late 1800s by studying diagrams of knots, which are projections of knots into a plane where the only singularities aretransverse double points, that is, places where two strands of the knot project to  transversely intersecting arcs. By labeling which arc comes from the “higher” part of the knot, one obtains a diagram from which the knot can be reconstructed. It is possible to treat all of knot theory as the study of such diagrams with the understanding that different diagrams that represent the same knot must be considered as equivalent diagrams.While it is simpler to allow only double points in the projection,  there is no reason not to allow n-fold singularities where n strands cross at a single point in the projection for larger values of n. These multicrossing  diagrams provide a different vantage point on the theory of knots have been studied extensively in the last several years. In this talk I will describe much of what is known about multi crossing diagrams focus on the case of 3-crossing diagrams, where all singularities are transverse triple points. I will describe a set of diagrammatic “moves” similar to the classical Reidemeister moves for classical diagrams  that allow one to pass between any two 3-crossing diagrams of the same link. This is joint work with Colin Adams Martin Palmer.