Knots
1st Edition
Published on 27. November 2013
IX, 417 pages
978-3-11-027078-5 (ISBN)
Description
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.
Reviews / Votes
"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 ReviewsMore details
Series
Edition
3rd fully revised and extended edition
Language
English
Place of publication
Berlin/Boston
Germany
Target group
Professional and scholarly
US School Grade: College Graduate Student
Illustrations
205 Abbildungen
205 ill.
File size
5,28 MB
ISBN-13
978-3-11-027078-5 (9783110270785)
Schweitzer Classification
Other editions
Persons
Gerhard Burde, Goethe University Frankfurt am Main, Germany; Heiner Zieschang ┼; Michael Heusener, Blaise Pascal University, France.
Content
1 - Preface to the First Edition [Seite 5]
2 - Preface to the Second Edition [Seite 7]
3 - Preface to the Third Edition [Seite 8]
4 - Contents [Seite 9]
5 - Chapter 1: Knots and isotopies [Seite 15]
6 - Chapter 2: Geometric concepts [Seite 30]
7 - Chapter 3: Knot groups [Seite 44]
8 - Chapter 4: Commutator subgroup of a knot group [Seite 68]
9 - Chapter 5: Fibered knots [Seite 85]
10 - Chapter 6: A characterization of torus knots [Seite 99]
11 - Chapter 7: Factorization of knots [Seite 111]
12 - Chapter 8: Cyclic coverings and Alexander invariants [Seite 125]
13 - Chapter 9: Free differential calculus and Alexander matrices [Seite 154]
14 - Chapter 10: Braids [Seite 175]
15 - Chapter 11: Manifolds as branched coverings [Seite 205]
16 - Chapter 12: Montesinos links [Seite 222]
17 - Chapter 13: Quadratic forms of a knot [Seite 252]
18 - Chapter 14: Representations of knot groups [Seite 280]
19 - Chapter 15: Knots, knot manifolds, and knot groups [Seite 315]
20 - Chapter 16: Bridge number and companionship [Seite 348]
21 - Chapter 17: The 2-variable skein polynomial [Seite 367]
22 - Appendix A: Algebraic theorems [Seite 379]
23 - Appendix B: Theorems of 3-dimensional topology [Seite 385]
24 - Appendix C: Table [Seite 389]
25 - Appendix D: Knot projections 01-949 [Seite 398]
26 - References [Seite 401]
27 - Author index [Seite 421]
28 - Glossary of Symbols [Seite 425]
29 - Index [Seite 427]
2 - Preface to the Second Edition [Seite 7]
3 - Preface to the Third Edition [Seite 8]
4 - Contents [Seite 9]
5 - Chapter 1: Knots and isotopies [Seite 15]
6 - Chapter 2: Geometric concepts [Seite 30]
7 - Chapter 3: Knot groups [Seite 44]
8 - Chapter 4: Commutator subgroup of a knot group [Seite 68]
9 - Chapter 5: Fibered knots [Seite 85]
10 - Chapter 6: A characterization of torus knots [Seite 99]
11 - Chapter 7: Factorization of knots [Seite 111]
12 - Chapter 8: Cyclic coverings and Alexander invariants [Seite 125]
13 - Chapter 9: Free differential calculus and Alexander matrices [Seite 154]
14 - Chapter 10: Braids [Seite 175]
15 - Chapter 11: Manifolds as branched coverings [Seite 205]
16 - Chapter 12: Montesinos links [Seite 222]
17 - Chapter 13: Quadratic forms of a knot [Seite 252]
18 - Chapter 14: Representations of knot groups [Seite 280]
19 - Chapter 15: Knots, knot manifolds, and knot groups [Seite 315]
20 - Chapter 16: Bridge number and companionship [Seite 348]
21 - Chapter 17: The 2-variable skein polynomial [Seite 367]
22 - Appendix A: Algebraic theorems [Seite 379]
23 - Appendix B: Theorems of 3-dimensional topology [Seite 385]
24 - Appendix C: Table [Seite 389]
25 - Appendix D: Knot projections 01-949 [Seite 398]
26 - References [Seite 401]
27 - Author index [Seite 421]
28 - Glossary of Symbols [Seite 425]
29 - Index [Seite 427]
