Synopses & Reviews
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 Contents
PrerequisitesChapter 1. Knots and Knot TypesChapter 2. The Fundamental GroupChapter 3. The Free GroupsChapter 4. Presentation of GroupsChapter 5. Calculation of Fundamental GroupsChapter 6. Presentation of a Knot GroupChapter 7. The Free Calculus and the Elementary IdealsChapter 8. The Knot PolynomialsChapter 9. Characteristic Properties of the Knot PolynomialsAppendix I. Differentiable Knots are TameAppendix II. Categories and groupoidsAppendix III. Proof of the van Kampen theoremGuide to the LiteratureBibliographyIndex