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Introduction to Knot Theoryby Richard H. Crowell
Synopses & ReviewsPublisher Comments:Hailed by the Bulletin of the American Mathematical Society as "a very welcome addition to the mathematical literature," this text is appropriate for advanced undergraduates and graduate students. Written by two internationally renowned mathematicians, its accessible treatment requires no previous knowledge of algebraic topology. Starting with basic definitions of knots and knot types, the text proceeds to examinations of fundamental and free groups. A survey of the historic foundation for the notion of group presentation is followed by a careful proof of the theorem of Tietze and several examples of its use. Subsequent chapters explore the calculation of fundamental groups, the presentation of a knot group, the free calculus and the elementary ideals, and the knot polynomials and their characteristic properties. The text concludes with three helpful appendixes and a guide to the literature. Synopsis:Appropriate for advanced undergraduates and graduate students, this text by two renowned mathematicians was hailed by the Bulletin of the American Mathematical Society as "a very welcome addition to the mathematical literature." 1963 edition. Synopsis:Appropriate for advanced undergraduates and graduate students, this text by two renowned mathematicians was hailed by the Bulletin of the American Mathematical Society as "a very welcome addition to the mathematical literature." 1963 edition. Table of ContentsPrerequisites Chapter 1. Knots and Knot Types Chapter 2. The Fundamental Group Chapter 3. The Free Groups Chapter 4. Presentation of Groups Chapter 5. Calculation of Fundamental Groups Chapter 6. Presentation of a Knot Group Chapter 7. The Free Calculus and the Elementary Ideals Chapter 8. The Knot Polynomials Chapter 9. Characteristic Properties of the Knot Polynomials Appendix I. Differentiable Knots are Tame Appendix II. Categories and groupoids Appendix III. Proof of the van Kampen theorem Guide to the Literature Bibliography Index What Our Readers Are SayingBe the first to add a comment for a chance to win!Product Details
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