E-Book Overview
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.
Knot theory has expanded enormously since the first edition of this book published in 1985. A special feature of this second completely revised and extended edition is the introduction to two new constructions of knot invariants, namely the Jones and homfly polynomials and the Vassiliev invariants.
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 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.
E-Book Content
de Gruyter Studies in Mathematics 5 Editors: Carlos Kenig · Andrew Ranicki · Michael Röckner de Gruyter Studies in Mathematics 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 Riemannian Geometry, 2nd rev. ed., Wilhelm P. A. Klingenberg Semimartingales, Michel Me´tivier Holomorphic Functions of Several Variables, Ludger Kaup and Burchard Kaup Spaces of Measures, Corneliu Constantinescu Knots, Gerhard Burde and Heiner Zieschang Ergodic Theorems, Ulrich Krengel Mathematical Theory of Statistics, Helmut Strasser Transformation Groups, Tammo tom Dieck Gibbs Measures and Phase Transitions, Hans-Otto Georgii Analyt