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纽结理论（英文版）

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作者：R.H.Crowell,R.H.Fox 著著

出版社：世界图书出版公司

出版时间：2000-12-1

I S B N：9787506200875

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Introduction to Knot Theory

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纽结理论（英文版）

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内容简介

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.

作者简介

Prerequisites
Chapter Ⅰ Knots and Knot Types
1.Definition of a knot
2.Tame versus wild knots
3.Knot projections
4.Isotopy type， amphichelral and invertible knots
Chapter Ⅱ The Fundamentel Group
Introduction
1.Paths and loops
2.Classes of paths and loops
3.Change of basepoint
4.Induced homomorphisms of fundamental groups
5.Fundamental group of the circle
Chapter Ⅲ The Free Groups
Introduction .
1.The free group F[]
2.Reduced words
3.Free groups
Chapter Ⅵ Presentation of Groups
Introduction
1.Retractions and deformations
2.Homotopy type
3.The van Kampen theorem
Chapter Ⅵ Presentation of a Knot Guoup
Chapter Ⅶ The Free Calculus and the Elementary Ideals
Chapter Ⅷ The Knot Polynomials
Chapter Ⅸ Characteristic Proerties of the Knot Polynomials
Appendix Ⅰ.Differentable Knots are Tame
Appendix Ⅱ.Categories and groupoids
Appendix Ⅲ.Proof of the van Kampen theorm
Guide to the Literature
Biliography
Index