Knots / / Gerhard Burde, Heiner Zieschang.

• Superior document: Title is part of eBook package: De Gruyter DG Studies in Mathematics eBook-Package
• VerfasserIn: Burde, Gerhard,; Zieschang, Heiner,
• Place / Publishing House: Berlin ;, Boston : : De Gruyter, , [2008]; ©2002
• Year of Publication: 2008
• Edition: 2nd revised and extended ed. 2003
• Language: English
• Series: De Gruyter Studies in Mathematics , 5
• Physical Description: 1 online resource (559 p.)

This book is an introduction to classical knot theory. Topics covered include: different constructions of knots, knot diagrams, knot groups, fibred knots, characterisation of torus knots, prime decomposition of knots, cyclic coverings and Alexander polynomials and modules together with the free differential calculus, braids, branched coverings and knots, Montesinos links, representations of knot groups, surgery of 3-manifolds and knots. Knot theory has expanded enormously since the first edition of this book published in 1985. A special feature of this second completely revised and extended edition is the introduction to two new constructions of knot invariants, namely the Jones and homfly polynomials and the Vassiliev invariants. The book contains many figures and some tables of invariants of knots. This comprehensive account is an indispensable reference source for anyone interested in both classical and modern knot theory. Most of the topics considered in the book are developed in detail; only the main properties of fundamental groups and some basic results of combinatorial group theory are assumed to be known. The text is accessible to advanced undergraduate and graduate students in mathematics.

Table of Contents

Frontmatter -- Contents -- Chapter 1. Knots and Isotopies -- Chapter 2. Geometric Concepts -- Chapter 3. Knot Groups -- Chapter 4. Commutator Subgroup of a Knot -- Group -- Chapter 5. Fibred Knots -- Chapter 6. A Characterization of Torus -- Knots -- Chapter 7. Factorization of Knots -- Chapter 8. Cyclic Coverings and Alexander -- Invariants -- Chapter 9. Free Differential Calculus and Alexander -- Matrices -- Chapter 10. Braids -- Chapter 11. Manifolds as Branched Coverings -- Chapter 12. Montesinos Links -- Chapter 13. Quadratic Forms of a Knot -- Chapter 14. Representations of Knot Groups -- Chapter 15. Knots, Knot Manifolds, and Knot -- Groups -- Chapter 16. The 2-variable skein polynomial -- Appendix A. Algebraic Theorems -- Appendix B. Theorems of 3-dimensional -- Topology -- Appendix C. Tables -- Appendix D. Knot Projections 01-949 -- Backmatter