k-width of knots and links
by Hyam Rubinstein
Abstract: This is joint work with Joel Hass and Abby Thompson. Classically, knots and links are studied using diagrams, which can be projections onto a plane, or slices of knots and links by a family of parallel planes. In both cases, a single projection or normal direction of the family of planes is chosen. We propose instead to study larger families of planes, choosing all normal directions lying in a fixed plane, or all possible normal directions or finally all planes and round spheres to slice a given knot or link. These family of planes have k parameters where k=1,2,3,4 and give rise to natural invariants. Some connections to the curvature of knots and links will be outlined, following ideas of Milnor.