Knot Theory RAP

When Th 2:00-2:50
Where Altgeld 345
Organizer Peter Brinkmann
Office Altgeld 309
Email brinkman@math.uiuc.edu

This RAP serves two purposes. First, we will discuss some of the basics of knot theory such as knot projections, types of knots, knot groups, etc., loosely based on some introductory texts (such as Adams, 'The Knot Book'; Crowell-Fox, 'Introduction to Knot Theory'; Burde-Zieschang, 'Knots'; Rolfsen, 'Knots and Links'; Kauffman, 'On Knots'). Second, the RAP will serve as a platform for talks about current research (such as Vassiliev invariants, geometric knot theory, and slalom knots). Please let me know if you would like to give a talk.

Date Speaker Title
08/30/2001  

Organizational meeting
09/06/2001 Peter Brinkmann

Introduction to knot theory
09/13/2001 Peter Brinkmann

Introduction to knot theory (cont.)
09/20/2001 Nadya Shirokova

Finite type knot invariants

We will discuss the axiomatics for the invariants of finite type, introduced by V.Vassiliev. We will study their properties and show that classical invariants, like Alexander-Conway polynomial can be decomposed over invariants of finite type.
09/27/2001 Katharine Preedy

Types of knots
10/04/2001 Nadya Shirokova

Finite type knot invariants (cont.)
10/11/2001 Elizabeth Denne

Torus knots

This talk will discuss presentations of knot groups, beginning with Rolfsen's approach to the fundamental group of the complement of a torus knot and ending with Wirtinger presentations.
10/18/2001 Elizabeth Denne

Torus knots (cont.)
10/25/2001 John Sullivan

Rational tangles and two-bridge knots

The bridge number of a knot was related by Milnor to its total curvature. Most (small) alternating knots have bridge number two. This important class can be best understood, following Conway, as numerators of rational tangles. These tangles, generated from the zero tangle by two simple moves, are in one-to-one correspondance with rational numbers, and are related to their continued fractions.
11/01/2001 John Sullivan

Rational tangles and two-bridge knots (cont.)
11/08/2001 George Francis

The Anatomy of the Figure-8 Knot Complement

I will describe visually intuitive ways of looking at knot-complements, their hyperbolic structure (when they have one), their foliation by Seifert surfaces and their monodromy. The figure-eight knot is our protagonist in this topological opera. Though most of the ideas are Thurston's, their pictures are most revealing.
11/15/2001 George Francis

The Anatomy of the Figure-8 Knot Complement (cont.)
11/22/2001 no meeting Thanksgiving break
11/29/2001 John Sullivan

Rational tangles and two-bridge knots (cont.)
12/06/2001  

Organizational meeting & Video presentation: "Not Knot" by Charlie Gunn
Peter Brinkmann
$Date: 2002-01-21 00:59:46-06 $

Valid HTML 4.01! Made with vi