Chapter 1: Knots and isotopies

Chapters in this book

1. Frontmatter i
2. Preface to the First Edition v
3. Preface to the Second Edition vii
4. Preface to the Third Edition viii
5. Contents ix
6. Chapter 1: Knots and isotopies 1
7. Chapter 2: Geometric concepts 16
8. Chapter 3: Knot groups 30
9. Chapter 4: Commutator subgroup of a knot group 54
10. Chapter 5: Fibered knots 71
11. Chapter 6: A characterization of torus knots 85
12. Chapter 7: Factorization of knots 97
13. Chapter 8: Cyclic coverings and Alexander invariants 111
14. Chapter 9: Free differential calculus and Alexander matrices 140
15. Chapter 10: Braids 161
16. Chapter 11: Manifolds as branched coverings 191
17. Chapter 12: Montesinos links 208
18. Chapter 13: Quadratic forms of a knot 238
19. Chapter 14: Representations of knot groups 266
20. Chapter 15: Knots, knot manifolds, and knot groups 301
21. Chapter 16: Bridge number and companionship 334
22. Chapter 17: The 2-variable skein polynomial 353
23. Appendix A: Algebraic theorems 365
24. Appendix B: Theorems of 3-dimensional topology 371
25. Appendix C: Table 375
26. Appendix D: Knot projections 0₁–9₄₉ 384
27. References 387
28. Author index 407
29. Glossary of Symbols 411
30. Index 413