An Introduction to Knot Theory

1. A Beginning for Knot Theory. - Exercises. - 2. Seifert Surfaces and Knot Factorisation. - Exercises. - 3. The Jones Polynomial. - Exercises. - 4. Geometry of Alternating Links. - Exercises. - 5. The Jones Polynomial of an Alternating Link. - Exercises. - 6. The Alexander Polynomial. - Exercises. - 7. Covering Spaces. - Exercises. - 8. The Conway Polynomial Signatures and Slice Knots. - Exercises. - 9. Cyclic Branched Covers and the Goeritz Matrix. - Exercises. - 10. The Arf Invariant and the Jones Polynomia. - Exercises. - 11. The Fundamental Group. - Exercises. - 12. Obtaining 3-Manifolds by Surgery on S3. - Exercises. - 13. 3-Manifold Invariants From The Jones Polynomial. - Exercises. - 14. Methods for Calculating Quantum Invariants. - Exercises. - 15. Generalisations of the Jones Polynomial. - Exercises. - 16. Exploring the HOMFLY and Kauffman Polynomials. - Exercises. - References. Language: English