Knots (eBook)

Gerhard Burde, Heiner Zieschang, Michael Heusener (Autoren)

eBook Download: PDF

2013 | 1., 3rd fully revised and extended edition
426 Seiten
De Gruyter (Verlag)
978-3-11-027078-5 (ISBN)

Infos

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.

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

Autor

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

Inhalt

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

Rezensionen

"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

Produkt-Details

• Erscheint lt. Verlag: 27.11.2013
• Reihe/Serie: De Gruyter Studies in Mathematics
• Reihe/Serie: De Gruyter Studies in Mathematics
• Reihe/Serie: ISSN
• Reihe/Serie: ISSN
• Zusatzinfo: 205 b/w ill.
• Verlagsort: Berlin/Boston
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik ► Allgemeines / Lexika
• Themenwelt: Mathematik / Informatik ► Mathematik ► Algebra
• Themenwelt: Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
• Themenwelt: Technik
• Schlagworte: Alexander Polynomials • braids • Branched Coverings • Cyclic Periods of Knots • Factorization • Fibred Knots • Homfly Polynomials • Knoten (Math.) • Knot Groups • knots • Links • Montesinos Links • Seifert Matrices • Seifert Surface
• ISBN-10: 3-11-027078-1 / 3110270781
• ISBN-13: 978-3-11-027078-5 / 9783110270785