Copies of the classnotes are on the internet in PDF format as given below. The "Proofs of Theorems" files were prepared in Beamer. The "Printout of Proofs" are printable PDF files of the Beamer slides without the pauses. These notes and supplements have not been classroom tested (and so may have some typographical errors). ETSU does not have a formal graduate class on knot theory, but these notes may be used in an Independent Study (MATH 5900).
Notes are available for a less rigorous class in knot theory. See my online page for Introduction to Knot Theory Class Notes based on Charles Livingston's Knot Theory, The Carus Mathematical Monographs, Volume 24 (MAA, 1993).
Preface. PDF
Chapter 1. A Beginning for Knot Theory.
Study Guide 1.
Chapter 2. Seifert Surfaces and Knot Factorisation
Study Guide 2.
Chapter 3. The Jones Polynomial.
Study Guide 3.
Chapter 4. A Geometry of Alternating Links.
Study Guide 4.
Chapter 5. The Jones Polynomial of an Alternating Link.
Study Guide 5.
Chapter 6. The Alexander Polynomial.
Study Guide 6.
Chapter 7. Covering Spaces.
Study Guide 7.
Chapter 8. The Conway Polynomial, Signatures and Slice Knots.
Study Guide 8.
Chapter 9. Cyclic Branched Covers and the Goeritz Matrix.
Study Guide 9.
Chapter 10. The Arf Invariant and the Jones Polynomial.
Study Guide 10.
Chapter 11. The Fundamental Group.
Study Guide 11.
Chapter 12. Obtaining 3-Manifolds by Surgery on S3.
Study Guide 12.
Chapter 13. 3-Manifold Invariants From the Jones Polynomial.
Study Guide 13.
Chapter 14. Methods for Calculating Quantum Invariants.
Study Guide 14.
Chapter 15. Generalizations of the Jones Polynomial.
Study Guide 15.
Chapter 16. Exploring the HOMFLY and Kauffman Polynomials.
Study Guide 16.
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