Quantum Topology / Hopf Algebra Seminar
Louis H Kauffman
UIC
Introduction to Knotoids and Virtual Knot Theory
Abstract: We discuss two generalizations of classical knot theory that are tightly related to each other.
A knotoid diagram is a projection of an open-ended arc embedded in three-dimensional space. Taking such a
diagram up to Reidemeister moves in the plane is equivalent to taking the arc up to isotopies that preserve the
projections of its endpoints. By choosing a single direction of projection, one obtains a subset of isotopies of
three-space that can 'measure' the topology of the embedded arc (with respect to that projection). Virtual knot
theory is the study of knots embedded in thickened surfaces. Knotoids can be studied by closing their endpoints
through the addition of a handle to the plane to produce a corresponding virtual knot of genus one.
Tuesday January 10, 2017 at 4:00 PM in SEO 612