Knot Groups. Annals of Mathematics Studies. (AM-56), Volume 56

Description

The description for this book, Knot Groups. Annals of Mathematics Studies. (AM-56), Volume 56, will be forthcoming. CONTENTS CHAPTER I: INTRODUCTION §1. Introduction CHAPTER II: NOTATION AND CONVENTIONS §1. Introduction §2. Group Theory §3. Geometric Conventions CHAPTER Ill: COMBINATORIAL COVERING SPACE THEORY FOR 3-MANIFOIDS §1. Introduction §2. Computation of π1 from a Maximal Cave §3. The Splitting Complex §4. A Splitting Complex for a Knot §5. Construction of Coverings from a Splitting Complex CHAPTER IV: THE COMMUTATOR SUBGROUP AND THE ALEXANDER MATRIX §1. Introduction §2. An Orientable Surface Spanned by a Knot §3. The Infinite Cyclic Covering of a Knot §4. A Property of the Surface of Minimal Genus §5. The Structure of the Commitator Subgroup of a Knot Group §6. The Alexander Matrix (tentative Description) §7. The Alexander Polynomials §8. The Alexander Matrix §9. The Alexander Polynomial CHAPTER V: SUBGROUPS §1. Introduction §2. Kernels of Maps to Zn §3. Kn/[Kn, Kn] §4 . Abelian Subgroups §5. Homology of Subgroups §6. Commutator and Central Series §7. Ends CHAPTER VI: REPRESENTATIONS §1. Introduction §2. Metacyclic Representations §3. Non-trivial Representations of Non-trivial Elements §4. The Range of Finite Homomorphs CHAPTER VII: AUTOMORPHISMS §1. Introduction §2. Outer Automorphisms §3. Symmetries CHAPTER VIII: A GROUP OF GROUPS §1. Introduction §2. The Semi-group of Knots §3. Some Axioms §4. A Binary Relation §5. Some Examples §6. Amalgamations §7. Knot Groups CHAPTER IX: THE CHARACTERIZATION PROBLEM §1. Introduction §2. Necessary and Sufficient Conditions §3. Sufficient Conditions §4. Necessary Conditions CHAPTER X: THE STRENGTH OF THE GROUP §1. Introduction §2. Homotopy Type §3. The Topological Type of the Complement of a Knot §4. Knot Type CHAPTER XI: PROBLEMS §1. Introduction §2. Problems APPENDIX BIBLIOGRAPHY INDEX