TY  - BOOK
AU  - Crowell,R. H.
TI  - Introduction to knot theory
SN  - 1461299373
U1  - 514.224 
PY  - 2011///
CY  - New York
PB  - Springer
KW  - Knot theory
N1  - Prerequisites.- I * 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 *; 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 * The Free Groups.- 
1. The free group F[A].- 
2. Reduced words.- 
3. Free groups.- 
IV * 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 * Calculation of Fundamental Groups.- 
1. Retractions and deformations.- 
2. Homotopy type.- 
3. The van Kampen theorem.- 
VI * 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 * The Free Calculus and the Elementary Ideals.- 
1. The group ring.- 
2. The free calculus.- 
3. The Alexander matrix.- 
4. The elementary ideals.- 
VIII * 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 * Characteristic Properties of the Knot Polynomials.- 
1. Operation of the trivialize.- 
2. Conjugation.- 
3. Dual presentations.-
ER  -