Author | Crowell, Richard H. author |
---|---|
Title | Introduction to Knot Theory [electronic resource] / by Richard H. Crowell, Ralph H. Fox |
Imprint | New York, NY : Springer New York, 1963 |
Connect to | http://dx.doi.org/10.1007/978-1-4612-9935-6 |
Descript | X, 182 p. online resource |
Prerequisites -- I ยท Knots and Knot Types -- 1. Definition of a knot -- 2. Tame versus wild knots -- 3. Knot projections -- 4. Isotopy type, amphicheiral and invertible knots -- II ยท; The Fundamental Group -- 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 -- III ยท The Free Groups -- 1. The free group F[A] -- 2. Reduced words -- 3. Free groups -- IV ยท Presentation of Groups -- 1. Development of the presentation concept -- 2. Presentations and presentation types -- 3. The Tietze theorem -- 4. Word subgroups and the associated homomorphisms -- 5. Free abelian groups -- V ยท Calculation of Fundamental Groups -- 1. Retractions and deformations -- 2. Homotopy type -- 3. The van Kampen theorem -- VI ยท Presentation of a Knot Group -- 1. The over and under presentations -- 2. The over and under presentations, continued -- 3. The Wirtinger presentation -- 4. Examples of presentations -- 5. Existence of nontrivial knot types -- VII ยท The Free Calculus and the Elementary Ideals -- 1. The group ring -- 2. The free calculus -- 3. The Alexander matrix -- 4. The elementary ideals -- VIII ยท The Knot Polynomials -- 1. The abelianized knot group -- 2. The group ring of an infinite cyclic group -- 3. The knot polynomials -- 4. Knot types and knot polynomials -- IX ยท Characteristic Properties of the Knot Polynomials -- 1. Operation of the trivialize -- 2. Conjugation -- 3. Dual presentations -- Appendix I. Differentiable Knots are Tame -- Appendix II. Categories and groupoids -- Appendix III. Proof of the van Kampen theorem -- Guide to the Literature