Knot Groups

Contents......Page 2
§ 1. Introduction......Page 4
§2. Group Theory......Page 7
§3. Geometric Conventions......Page 8
§2. Computation of n from a Maximal Cave......Page 11
§3. The Splitting Complex......Page 14
§4. A Splitting Complex for a Knot......Page 15
§5. Construction of Coverings from a Splitting Complex......Page 17
§2. An Orientable Surface Spanned by a Knot......Page 26
§3. The Infinite Cyclic Covering of a Knot......Page 27
§4. A Property of the Surface of Minimal Genus......Page 28
§5. The Structure of the Commutator Subgroup of a Knot Group......Page 30
§7. The Alexander Polynomials......Page 35
§8. The Alexander Matrix......Page 43
§9. The Alexander Polynomial......Page 47
§2. Kernels of Maps to Z_n......Page 50
§3. K_n / [K_n, K_n]......Page 52
§4. Abelian Subgroups......Page 57
§5. Homology of Subgroups......Page 59
§7. Ends......Page 60
§2. Metacyclic Representations......Page 61
§3. Non-trivial Representations of Non-trivial Elements......Page 63
§4. The Range of Finite Homomorphs......Page 65
§1. Introduction......Page 66
§2. Outer Automorphisms......Page 68
§3. Symmetries......Page 71
§1. Introduction......Page 74
§2. The Semi-group of Knots......Page 75
§3. Some Axioms......Page 76
§4. A Binary Relation......Page 77
§5. Some Examples......Page 80
§6. Amalgamations......Page 82
§7. Knot Groups......Page 83
§2. Necessary and Sufficient Conditions......Page 86
§3. Sufficient Conditions......Page 89
§4. Necessary Conditions......Page 90
§2. Homotopy Type......Page 92
§3. The Topological Type of the Complement of a Knot......Page 93
§4. Knot Type......Page 96
§2. Problems......Page 98
Appendix by S. Eilenberg......Page 102
Bibliography......Page 105
Index......Page 110