This volume is an introduction to Knot Theory. It includes a selection of topics which graduate students have found to be a successful introduction to the field and employs three distinct techniques; Algebraic Topology, Combinatorics, and Algebraic Topology. Each topic is developed until a significant result is achieved and chapters end with exercises and brief accounts of state-of-the-art research.

Written by an internationally acknowledged expert in the field who has won prizes for both exposition and research Gives a comprehensive introduction to the field, presenting modern developments in the context of classical material Will appeal to graduate students, mathematicians and physicists with a mathematical background who wish to gain new insights in this area

Inhalt

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.