1. A Survey of Knots and Links
Matt Lawson
Appalachian State University
8 December 2001

2. Abstract
A summary of knots and knot theory, starting with a definition of what a knot is (what makes a knot a knot) and leading into to the motivation for a knot invariant. An important part of this is a discussion of the Redermeister moves, which preserve knot invariants (such as coloring). The topological significance of the knot will also be covered. The latter part of the talk will delve into knot algebras and possible applications of knot theory to fields in physics and biology. Lastly a catalogue of knots will be displayed, and, if time permits, the program KnotPlot by Rob Scharein will be demonstrated.

3. What Is a Knot? An embedding of S1 into R3
Mathematical knot vs. knot on a string
Knot (and link) vs. knot diagram vs. knot projection

4. Some Examples of Knots
Note the similarity between the trefoil and unknot#2. Suggests uncrossing no.

5. Examples of Links

6. Knot Theory-Knots and Links
Problem 1: How do you prove the trefoil is knotted?
Crossings: the heart of knots

7. The Redermeister Moves
how to untangle a knot
Type I – the untwist
Type II – ±2 crossings
Type III -- sliding

8. Illustrated Redermeister Moves
Don’t forget about R0 and R4