Zieschang / Burde Knots

2. revised and extended Auflage 2003
ISBN: 978-3-11-019803-4
Verlag: De Gruyter
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, Band 5, 571 Seiten, Gewicht: 10 g

Reihe: De Gruyter Studies in Mathematics

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.

Autoren/Hrsg.

Zieschang, Heiner

Burde, Gerhard

Fachgebiete

• Mathematik | Informatik Mathematik Geometrie
• Mathematik | Informatik Mathematik Topologie

Inhaltsverzeichnis

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