This document provides an introduction to knot theory, covering its history, different types of knots including braids and links, properties like handedness, knot invariants such as the Alexander-Conway polynomial, and applications including modeling chirality in molecules and DNA and potential uses in quantum computing. It discusses key topics like the unknot, the trefoil knot, and Reidemeister moves.

1. Knot Theory
An introduction

2. A brief history of
knots

3. A false start

4. Take 2

5. Types of knot
Braids Links

6. The Unknot

7. The Trefoil
Left-handed Right-handed

8. Knot Invariants

9. Reidermeister Moves
I II III

10. The Alexander-
Conway Polynomial
C(L+) = C(L-) + zC(L0)

11. A worked example
C( ) = C( ) + zC( )
C( ) = C( ) + zC( )
C( ) = C( ) + zC( )
C( ) = 1 + z(0 + z)

12. Chirality of molecules

13. DNA

14. Quantum Computing
?!?