纽结理论

　　This book was written as an introductory text for a one semester course and， as such， it is far from a comprehensive reference work. Its lack of completeness is now more apparent than ever since， like most branches of mathematics， knot theory has expanded enormously during the last fifteen years. The book could certainly be rewritten by including more material and also by introducing topics in a more elegant and up-to-date style. Accomplishing these objectives would be extremely worthwhile. However， a significant revision of the original work along these lines， as opposed to writing a new book， would probably be a mistake. As inspired by its senior author， the late Ralph H. Fox， this book achieves qualities of effectiveness， brevity， elementary character， and unity. These characteristics would be jeopardized， if not lost， in a major revision. As a result， the book is being republished unchanged， except for minor corrections. The most important of these occurs in Chapter III， where the old sections 2 and 3 have been interchanged and somewhat modified. The original proof of the theorem that a group is free if and only if it is isomorphic to F[] for some alphabet contained an error， which has been corrected using the fact that equivalent reduced words are equal.本书为英文版。

暂缺《纽结理论》作者简介

Prerequisites
ChapterIKnotsandKnotTypes
1.Definitionofaknot
2.Tameversuswildknots
3.Knotprojections
4.Isotopytype,amphichelralandinvertibleknots
ChapterIITheFundamentelGroup
Introduction
1.Pathsandloops
2.Classesofpathsandloops
3.Changeofbasepoint
4.Inducedhomomorphismsoffundamentalgroups
5.Fundamentalgroupofthecircle
ChapterIIITheFreeGroups
Introduction.
1.ThefreegroupF[]
2.Reducedwords
3.Freegroups
ChapterIVPresentationofGroups
Introduction
1.Developmentofthepresentationconcept
2.Presentationsandpresentationtypes
3.TheTietzetheorem
4.Wordsubgroupsandtheassociatedhomomorphisms
5.Freeabeliangroups
ChapterVCalculationofFundamentalGroups
Introduction
1.Retractionsanddeformations
2.Homotopytype
3.ThevanKampentheorem
ChapterVIPresentationofaKnotGroup
Introduction
1.Theoverandunderpresentations
2.Theoverandunderpresentations,continued
3.TheWirtingerpresentation
4.Examplesofpresentations
5.Existenceofnontrivialknottypes
ChapterVIITheFreeCalculusandtheElementaryIdeals
Introduction
1.Thegroupring
2.Thefreecalculus
3.TheAlexandermatrix
4.Theelementaryideals
ChapterVIIITheKnotPolynomials
Introduction
1.Theabelianizedknotgroup
2.Thegroupringofaninfinitecyclicgroup
3.Theknotpolynomials
4.Knottypesandknotpolynomials
ChapterIXCharacteristicPropertiesoftheKnotPolynomials
Introduction
1.Operationofthetrivializer
2.Conjugation
3.Dualpresentations
AppendixI.DifferentiableKnotsareTame
AppendixII.Categoriesandgroupoids
AppendixIII.ProofofthevanKampentheorem
GuidetotheLiterature
Bibliography
Index