Knots

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.

About the author

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

Report

"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

Product details

• Authors: Gerhar Burde, Gerhard Burde, Michael Heusener, Heine Zieschang, Heiner Zieschang
• Publisher: De Gruyter
• Languages: English
• Product format: Hardback
• Released: 01.11.2013
• EAN: 9783110270747
• ISBN: 978-3-11-027074-7
• No. of pages: 417
• Dimensions: 166 mm x 28 mm x 240 mm
• Weight: 854 g
• Illustrations: 205 b/w ill.
• Series: Gruyter - de Gruyter Studies in Mathematics; De Gruyter Studies in Mathematics; De Gruyter Studies in Mathematics; ISSN
• Subjects: Natural sciences, medicine, IT, technology > Mathematics > Geometry; Mathematik, Geometrie, Enzyklopädie, Nachschlagewerke, Gruppe (mathematisch) - Gruppentheorie, Angewandte Mathematik, Gruppen und Gruppentheorie, Algebra / Gruppe (mathematisch), Topologie, Topologie - Differenzialtopologie, Raumlehre, MATHEMATICS / Geometry / General, Knoten (Math.); Links; Fibred Knots; Factorization; Braids; Branched Coverings; Montesinos Links; Knot Groups; Seifert Surface; Alexander Polynomials; Seifert Matrices; Cyclic Periods of Knots; Homfly Polynomials