Knots
Electronic books Knot theory Nœuds, Théorie des MATHEMATICS sähkökirjat Knoten 28
de Gruyter
2003
2., rev. and extended ed
EISBN 9783110198034
Chapter 14Representations of Knot GroupsChapter 15Knots, Knot Manifolds, and Knot Groups; Chapter 16The 2-variable skein polynomial; Appendix AAlgebraic Theorems; Appendix BTheorems of 3-dimensional Topology; Appendix CTables; Appendix DKnot Projections 01-949; Bibliography; List of Authors According to Codes; Author Index; Subject Index.
de Gruyter Studies in Mathematics; Preface to the First Edition; Preface to the Second Edition; Contents; Chapter 1Knots and Isotopies; Chapter 2Geometric Concepts; Chapter 3Knot Groups; Chapter 4Commutator Subgroup of a Knot Group; Chapter 5Fibred Knots; Chapter 6A Characterization of Torus Knots; Chapter 7Factorization of Knots; Chapter 8Cyclic Coverings and Alexander Invariants; Chapter 9Free Differential Calculus and Alexander Matrices; Chapter 10Braids; Chapter 11Manifolds as Branched Coverings; Chapter 12Montesinos Links; Chapter 13Quadratic Forms of a Knot.
Main description: 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.
de Gruyter Studies in Mathematics; Preface to the First Edition; Preface to the Second Edition; Contents; Chapter 1Knots and Isotopies; Chapter 2Geometric Concepts; Chapter 3Knot Groups; Chapter 4Commutator Subgroup of a Knot Group; Chapter 5Fibred Knots; Chapter 6A Characterization of Torus Knots; Chapter 7Factorization of Knots; Chapter 8Cyclic Coverings and Alexander Invariants; Chapter 9Free Differential Calculus and Alexander Matrices; Chapter 10Braids; Chapter 11Manifolds as Branched Coverings; Chapter 12Montesinos Links; Chapter 13Quadratic Forms of a Knot.
Main description: 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.
