1. Linking number
Smallest number of crossing changes that make a link splittable
Lk(K)=Tw(K)+Wr(K)
Analogous to unknotting no. eqn used in DNA research… defines linking no for a knot. Stronger invariant

2. Seifert Spanning Surfaces
One of the stronger knot invariants
Looking at the space “covered” by a knot
Preserved under homeomorphism
Bubble film analogy

3. Plane homeo to hollow box

4. Knot Polynomials ways to represent a knot algebraically
Bracket and Jones polynomials
Conway, Alexander, HOMFLY polynomials
Kauffman polynomial
Alexander is the oldest. Kauffman c Bracket has alaogy to statmech partition function

5. Knot Algebras Knot Groups
Quaternion groups and the "Type IV Redermeister move"
Tensor calculus using knots
Not much detail… quite intimidating… same processes different notations and applications
Commutative and non-commutative operations

6. Applications Biology-the knotting of DNA strands Physics
Conductance
Yang-Baxter equations
The Lorentz attractor as a knot
Atoms were postulated to be knotted vortices [KP,5]. Knotting-unknotting may explain how enzymes work in the body

7. Summary
Recap of Knot Theory
Why Knot Theory?

8. Catalog of Knots and Knot Nomenclature
Arbitrary system from late 1800’s
Apparently classified by number of crossings

11. Knots On the Web
Scharein, Robert G. The KnotPlot Site. Oct
Real Knots: Knotting, bends and hitches. May 2000.
Ideas, Concepts, and Definitions.

12. Bibliography
Adams, Colin. The Knot Book. New York: W.H Freeman and Co., 1994
Farmer, David W. and Theodore B. Stanford. Knots and Surfaces. American Mathematical Society, 1996.
Gilbert, N. D. and T. Porter. Knots and Surfaces. New York: Oxford University Press, 1994.
Kauffman, Louis. Knots and Physics, Second Ed. New Jersey: World Scientific, On Knots. New Jersey: Princeton University Press, 1987.
Prasilov, V.V. Intuitive Topology. American Mathematical Society, 1995.

13. KnotPlot Demonstration
Zoo and relaxations