Knots

Gerhard Burde; Heiner Zieschang; Michael Heusener

Published by De Gruyter 2013

Knots

Gerhard Burde , Heiner Zieschang and Michael Heusener

Volume 5 in the series De Gruyter Studies in Mathematics

https://doi.org/10.1515/9783110270785

Overview
Contents

About this book

This 3. edition is an introduction to classical knot theory. It 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.

Author / Editor information

Gerhard Burde, Goethe University Frankfurt am Main, Germany; Heiner Zieschang †; Michael Heusener, Blaise Pascal University, France.

Reviews

"Gerhard Burde and Heiner Zieschang's Knots has been an excellent reference for students of classical knot theory since it was first published in 1985." Mathematical Reviews

Supplementary Materials

Contents

Topics

Frontmatter Publicly Available Download PDF	i
Preface to the First Edition Requires Authentication Unlicensed Licensed Download PDF	v
Preface to the Second Edition Requires Authentication Unlicensed Licensed Download PDF	vii
Preface to the Third Edition Requires Authentication Unlicensed Licensed Download PDF	viii
Contents Publicly Available Download PDF	ix
Chapter 1: Knots and isotopies Requires Authentication Unlicensed Licensed Download PDF	1
Chapter 2: Geometric concepts Requires Authentication Unlicensed Licensed Download PDF	16
Chapter 3: Knot groups Requires Authentication Unlicensed Licensed Download PDF	30
Chapter 4: Commutator subgroup of a knot group Requires Authentication Unlicensed Licensed Download PDF	54
Chapter 5: Fibered knots Requires Authentication Unlicensed Licensed Download PDF	71
Chapter 6: A characterization of torus knots Requires Authentication Unlicensed Licensed Download PDF	85
Chapter 7: Factorization of knots Requires Authentication Unlicensed Licensed Download PDF	97
Chapter 8: Cyclic coverings and Alexander invariants Requires Authentication Unlicensed Licensed Download PDF	111
Chapter 9: Free differential calculus and Alexander matrices Requires Authentication Unlicensed Licensed Download PDF	140
Chapter 10: Braids Requires Authentication Unlicensed Licensed Download PDF	161
Chapter 11: Manifolds as branched coverings Requires Authentication Unlicensed Licensed Download PDF	191
Chapter 12: Montesinos links Requires Authentication Unlicensed Licensed Download PDF	208
Chapter 13: Quadratic forms of a knot Requires Authentication Unlicensed Licensed Download PDF	238
Chapter 14: Representations of knot groups Requires Authentication Unlicensed Licensed Download PDF	266
Chapter 15: Knots, knot manifolds, and knot groups Requires Authentication Unlicensed Licensed Download PDF	301
Chapter 16: Bridge number and companionship Requires Authentication Unlicensed Licensed Download PDF	334
Chapter 17: The 2-variable skein polynomial Requires Authentication Unlicensed Licensed Download PDF	353
Appendix A: Algebraic theorems Requires Authentication Unlicensed Licensed Download PDF	365
Appendix B: Theorems of 3-dimensional topology Requires Authentication Unlicensed Licensed Download PDF	371
Appendix C: Table Requires Authentication Unlicensed Licensed Download PDF	375
Appendix D: Knot projections 0₁–9₄₉ Requires Authentication Unlicensed Licensed Download PDF	384
References Requires Authentication Unlicensed Licensed Download PDF	387
Author index Requires Authentication Unlicensed Licensed Download PDF	407
Glossary of Symbols Requires Authentication Unlicensed Licensed Download PDF	411
Index Requires Authentication Unlicensed Licensed Download PDF	413

(Deutsch)

Language: English
Publisher: De Gruyter
Edition: 3rd fully revised and extended edition
Audience: Advanced Undergraduate and Graduate Students in Mathematics, Researchers; Academic Libraries
Pages
- Front matter: 9
- Main content: 417
Illustrations
- Illustrations: 205
Keywords: Knots; Links; Fibred Knots; Factorization; Braids; Branched Coverings; Montesinos Links; Knot Groups; Seifert Surface; Alexander Polynomials; Seifert Matrices; Cyclic Periods of Knots; Homfly Polynomials

eBook

Published: November 27, 2013
ISBN: 9783110270785

Hardcover

Published: November 15, 2013
ISBN: 9783110270747