Knot Theory

• Required text:
  • Title: Knot Theory
  • Author: Charles Livingston
  • ISBN: 0883850273
  • Publisher: The Mathematical Association of America
  • Amazon.com page for ordering it

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1. Install Mozilla from Page for obtaining the Mozilla browser
   It will also be necessary to install math fonts for this browser. Information on how to install these can be found on
   The MathML Fonts Page
   For linux users, the necessary fonts can be found in: mozilla-math.tar.gz (these should be installed in X windows).

Note: Other web pages for this course will not necessarily even show up in other browsers! Once you have installed Mozilla and the fonts, you can check your installation by viewing:

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Topics

1. Introduction: A century of Knot Theory
2. What is a knot?
   • Wild Knots and unknottings
   • Definition of a knot
   • Equivalence of knots: deformations
   • Diagrams and projections
   • Orientation
   • Links
3. Invariants of knots
   • crossing number
   • bridge number
   • genus
   • colorability
4. Polynomial Invariants
   • Alexander polynomial
   • Bracket polynomial

Homework

1. Chapter 2. p. 19: 3.1,3.2, 3.4;p. 26 5.2

Computing the Alexander Polynomial from knot groups

The MathML Start Page

Use this to check whether MathML is working properly on your web browser. Unfortunately, the Windows version of Mozilla seems to have a bug that will cause it to complain about missing fonts even though the fonts are there (and Mozilla is using them correctly).

Lecture Notes

1. 3-30-2004
2. 4-1-2004
3. 4-8-2004
4. 4-13-2004
5. 4-15-2004
6. 4-20-2004
7. 4-22-2004
8. 4-27-2004
9. 4-29-2004
10. 5-3-2004
11. 5-11-2004
12. 5-13-2004
13. 5-18-2004
14. 5-25-2004
15. 6-1-2004

Links

• Knot Table
• Knotilius Site
• Reidemeister Moves
• Knot Invariants
• Knot Theory Home Page
• The Geometry Junkyard Knot Theory page
• Applied Abstract Algebra Home Page
• KnotPlot software
• Some knots used in basic seamanship
• The braid group
• Animation of braid group multiplication
• Cryptography and braid groups

Exam Schedule

1. Exam 1, Week 3
2. Exam 2, Week 6
3. Exam 3, Week 9

Homework

• Assignment 2: p. 35 2.1, 2.2, p. 36 2.4, 2.5 p. 48 4.2
• Assignment 3: p. 60 1.1, 1.2, 1.3
• Assignment 4: p. 68 2.1, 2.5, 2.9; p. 81 5.2
• Assignment 5: p. 98 3.1, 3.2 3.3; p. 104 4.1, 4.2