Knots / Gerhard Burde, Heiner Zieschang.

Format:

Book

Author/Creator:

Burde, Gerhard, 1931-

Contributor:

Zieschang, Heiner.

Series:

Gruyter studies in mathematics ; 5.

De Gruyter studies in mathematics ; 5

Language:

English

Subjects (All):

Algebraic topology.

Topology.

Physical Description:

1 online resource (572 p.)

Edition:

2nd rev. and extended ed.

Place of Publication:

Berlin ; New York : Walter de Gruyter, 2003.

Language Note:

English

Summary:

This book is an introduction to classical knot theory. Topics covered include: different constructions of knots, knot diagrams, knot groups, fibered 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

Contents:

Front matter

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

Back matter

Notes:

Description based upon print version of record.

Includes bibliographical references (p. [367]-505) and indexes.

Part of the metadata in this record was created by AI, based on the text of the resource.

ISBN:

1-282-19430-5

9786612194306

3-11-019803-7

OCLC:

437191145