Burde / Zieschang / Heusener Knots

3rd fully revised and extended Auflage
ISBN: 978-3-11-027078-5
Verlag: De Gruyter
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 426 Seiten

Reihe: ISSN

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, Jones and HOMFLYPT polynomials.

Knot theory has expanded enormously since the first edition of this book published in 1985. In this third completely revised and extended edition a chapter about bridge number and companionship of knots has been added.

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, covering spaces 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.

Zielgruppe

Advanced Undergraduate and Graduate Students in Mathematics, Researchers; Academic Libraries

Autoren/Hrsg.

Burde, Gerhard

Zieschang, Heiner

Heusener, Michael

Fachgebiete

• Mathematik | Informatik Mathematik Topologie
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle

Inhaltsverzeichnis

1;Preface to the First Edition;5
2;Preface to the Second Edition;7
3;Preface to the Third Edition;8
4;Contents;9
5;Chapter 1: Knots and isotopies;15
6;Chapter 2: Geometric concepts;30
7;Chapter 3: Knot groups;44
8;Chapter 4: Commutator subgroup of a knot group;68
9;Chapter 5: Fibered knots;85
10;Chapter 6: A characterization of torus knots;99
11;Chapter 7: Factorization of knots;111
12;Chapter 8: Cyclic coverings and Alexander invariants;125
13;Chapter 9: Free differential calculus and Alexander matrices;154
14;Chapter 10: Braids;175
15;Chapter 11: Manifolds as branched coverings;205
16;Chapter 12: Montesinos links;222
17;Chapter 13: Quadratic forms of a knot;252
18;Chapter 14: Representations of knot groups;280
19;Chapter 15: Knots, knot manifolds, and knot groups;315
20;Chapter 16: Bridge number and companionship;348
21;Chapter 17: The 2-variable skein polynomial;367
22;Appendix A: Algebraic theorems;379
23;Appendix B: Theorems of 3-dimensional topology;385
24;Appendix C: Table;389
25;Appendix D: Knot projections 0–9;398
26;References;401
27;Author index;421
28;Glossary of Symbols;425
29;Index;427

Über Autor(innen)

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