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INTRODUCTION TO KNOT THEORYPDF|Epub|txt|kindle电子书版本网盘下载
- RICHARD H. CROWELL RALPH H. FOX 著
- 出版社： SPRINGER-VERLAG NEW YORK HEIDELBERG BERLIN
- ISBN：
- 出版时间：未知
- 标注页数：182页
- 文件大小：8MB
- 文件页数：190页
- 主题词：
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图书目录
Prerequisites1
Chapter Ⅰ Knots and Knot Types3
1.Definition of a knot3
2.Tame versus wild knots5
3.Knot projections6
4.Isotopy type,amphicheiral and invertible knots8
Chapter Ⅱ The Fundamental Group13
Introduction13
1.Paths and loops14
2.Classes of paths and loops15
3.Change of basepoint21
4.Induced homomorphisms of fundamental groups22
5.Fundamental group of the circle24
Chapter Ⅲ The Free Groups31
Introduction31
1.The free group F[？]31
2.Reduced words32
3.Free groups35
Chapter Ⅳ Presentation of Groups37
Introduction37
1.Development of the presentation concept37
2.Presentations and preeentation types39
3.The Tietze theorem43
4.Word subgroups and the associated homomorphisms47
5.Free abelian groups50
Chapter Ⅴ Calculation of Fundamental Groups52
Introduction52
1.Retractions and deformations54
2.Homotopy type62
3.The van Kampen theorem63
Chapter Ⅵ Presentation of a Knot Group72
Introduction72
1.The over and under presentations72
2.The over and under presentations,continued78
3.The Wirtinger presentation86
4.Examples of presentations87
5.Existence of nontrivial knot types90
Chapter Ⅶ The Free Calculus and the Elementary Ideals94
Introduction94
1.The group ring94
2.The free calculus96
3.The Alexander matrix100
4.The elementary ideals101
Chapter Ⅷ The Knot Polynomials110
Introduction110
1.The abelianized knot group111
2.The group ring of an infinite cyclic group113
3.The knot polynomials119
4.Knot types and knot polynomials123
Chapter Ⅸ Characteristic Properties of the Knot Polynomials134
Introduction134
1.Operation of the trivializer134
2.Conjugation136
3.Dual presentations137
Appendix Ⅰ.Differentiable Knots are Tame147
Appendix Ⅱ.Categories and groupeids153
Appendix Ⅲ.Proof of the van Kampen theorem156
Guide to the Literature161
Bibliography165
Index178