紐結(jié)理論

內(nèi)容概要

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.

書籍目錄

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 theoremChapter Ⅵ Presentation of a Knot GuoupChapter Ⅶ The Free Calculus and the Elementary IdealsChapter Ⅷ The Knot PolynomialsChapter Ⅸ Characteristic Proerties of the Knot PolynomialsAppendix Ⅰ.Differentable Knots are TameAppendix Ⅱ.Categories and groupoidsAppendix Ⅲ.Proof of the van Kampen theormGuide to the LiteratureBiliographyIndex

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