دانلود کتاب Knots, Links and Their Invariants: An Elementary Course in Contemporary Knot Theory

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Front Cover
Half Title
Title
Copyright
Contents
Foreword
Permissions & Acknowledgments
Lecture 1. Knots and Links, Reidemeister Moves
1.1. Main definitions
1.2. Reidemeister moves
1.3. Torus knots
1.4. Invertibility and chirality
1.5. Exercises
Lecture 2. The Conway Polynomial
2.1. Axiomatic definition
2.2. Calculations
2.3. Uniqueness and existence of the Conway polynomial
2.4. Chirality, orientation-reversal, and multiplicativity of the Conway polynomial
2.5. Exercises
Lecture 3. The Arithmetic of Knots
3.1. Boxed knots and their connected sum
3.2. The semigroup of boxed knots
3.3. Ordinary knots vs. boxed knots
3.4. Decomposition into prime knots
3.5. Some remarks about unknotting
3.6. Exercises
Lecture 4. Some Simple Knot Invariants
4.1. Stick number
4.2. Crossing number
4.3. Unknotting number
4.4. Tricolorability
4.5. Digression about orientable surfaces
4.6. Seifert surface of a knot
4.7. The genus of a knot
4.8. Exercises
Lecture 5. The Kauffman Bracket
5.1. Digression: statistical models in physics
5.2. The “state” of a (nonoriented) knot diagram
5.3. Definition and properties of the Kauffman bracket
5.4. Is the Kauffman bracket invariant?
5.5. Exercises
Lecture 6. The Jones Polynomial
6.1. Definition via the Kauffman bracket
6.2. Main properties of