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an introduction to the colored jones polynomial · it maps a diagram d of a link l to (d) e a—i]...

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An Introduction to The Colored Jones Polynomial LSU Math Geaux Seminar Mustafa Hajij

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Page 1: An Introduction to The Colored Jones Polynomial · It maps a diagram D of a link L to (D) e A—I] and it is characterized by the three rules: (ii) DU . The bracket polynomial is

An Introduction to The Colored Jones Polynomial

LSU Math Geaux Seminar Mustafa Hajij

Page 2: An Introduction to The Colored Jones Polynomial · It maps a diagram D of a link L to (D) e A—I] and it is characterized by the three rules: (ii) DU . The bracket polynomial is

Basic Definitions

Page 3: An Introduction to The Colored Jones Polynomial · It maps a diagram D of a link L to (D) e A—I] and it is characterized by the three rules: (ii) DU . The bracket polynomial is

Basic Definitions

Page 4: An Introduction to The Colored Jones Polynomial · It maps a diagram D of a link L to (D) e A—I] and it is characterized by the three rules: (ii) DU . The bracket polynomial is

Basic Definitions

Page 5: An Introduction to The Colored Jones Polynomial · It maps a diagram D of a link L to (D) e A—I] and it is characterized by the three rules: (ii) DU . The bracket polynomial is

Basic Definitions

Page 6: An Introduction to The Colored Jones Polynomial · It maps a diagram D of a link L to (D) e A—I] and it is characterized by the three rules: (ii) DU . The bracket polynomial is

Basic Definitions

Page 7: An Introduction to The Colored Jones Polynomial · It maps a diagram D of a link L to (D) e A—I] and it is characterized by the three rules: (ii) DU . The bracket polynomial is

Reidemeister's Theorem

Page 8: An Introduction to The Colored Jones Polynomial · It maps a diagram D of a link L to (D) e A—I] and it is characterized by the three rules: (ii) DU . The bracket polynomial is

Reidemeister's Theorem

Page 9: An Introduction to The Colored Jones Polynomial · It maps a diagram D of a link L to (D) e A—I] and it is characterized by the three rules: (ii) DU . The bracket polynomial is

Reidemeister's Theorem

Page 10: An Introduction to The Colored Jones Polynomial · It maps a diagram D of a link L to (D) e A—I] and it is characterized by the three rules: (ii) DU . The bracket polynomial is

Knot Invariants

Page 11: An Introduction to The Colored Jones Polynomial · It maps a diagram D of a link L to (D) e A—I] and it is characterized by the three rules: (ii) DU . The bracket polynomial is

Knot Invariants

Page 12: An Introduction to The Colored Jones Polynomial · It maps a diagram D of a link L to (D) e A—I] and it is characterized by the three rules: (ii) DU . The bracket polynomial is

Knot Invariants

Page 13: An Introduction to The Colored Jones Polynomial · It maps a diagram D of a link L to (D) e A—I] and it is characterized by the three rules: (ii) DU . The bracket polynomial is

Polynomial Knot Invariants

Page 14: An Introduction to The Colored Jones Polynomial · It maps a diagram D of a link L to (D) e A—I] and it is characterized by the three rules: (ii) DU . The bracket polynomial is

Polynomial Knot Invariants

Page 15: An Introduction to The Colored Jones Polynomial · It maps a diagram D of a link L to (D) e A—I] and it is characterized by the three rules: (ii) DU . The bracket polynomial is

The Jones Polynomial

Page 16: An Introduction to The Colored Jones Polynomial · It maps a diagram D of a link L to (D) e A—I] and it is characterized by the three rules: (ii) DU . The bracket polynomial is

The Jones Polynomial

Page 17: An Introduction to The Colored Jones Polynomial · It maps a diagram D of a link L to (D) e A—I] and it is characterized by the three rules: (ii) DU . The bracket polynomial is

The Jones Polynomial

Page 18: An Introduction to The Colored Jones Polynomial · It maps a diagram D of a link L to (D) e A—I] and it is characterized by the three rules: (ii) DU . The bracket polynomial is

Example

Page 19: An Introduction to The Colored Jones Polynomial · It maps a diagram D of a link L to (D) e A—I] and it is characterized by the three rules: (ii) DU . The bracket polynomial is

Example

Page 20: An Introduction to The Colored Jones Polynomial · It maps a diagram D of a link L to (D) e A—I] and it is characterized by the three rules: (ii) DU . The bracket polynomial is

The Temperly-Lieb Algebra

Page 21: An Introduction to The Colored Jones Polynomial · It maps a diagram D of a link L to (D) e A—I] and it is characterized by the three rules: (ii) DU . The bracket polynomial is

The Temperly-Lieb Algebra

Page 22: An Introduction to The Colored Jones Polynomial · It maps a diagram D of a link L to (D) e A—I] and it is characterized by the three rules: (ii) DU . The bracket polynomial is

The Temperly-Lieb Algebra

Page 23: An Introduction to The Colored Jones Polynomial · It maps a diagram D of a link L to (D) e A—I] and it is characterized by the three rules: (ii) DU . The bracket polynomial is

The Temperly-Lieb Algebra

Page 24: An Introduction to The Colored Jones Polynomial · It maps a diagram D of a link L to (D) e A—I] and it is characterized by the three rules: (ii) DU . The bracket polynomial is

The Temperly-Lieb Algebra

Page 25: An Introduction to The Colored Jones Polynomial · It maps a diagram D of a link L to (D) e A—I] and it is characterized by the three rules: (ii) DU . The bracket polynomial is

The Temperly-Lieb Algebra

Page 26: An Introduction to The Colored Jones Polynomial · It maps a diagram D of a link L to (D) e A—I] and it is characterized by the three rules: (ii) DU . The bracket polynomial is

The Temperly-Lieb Algebra

Page 27: An Introduction to The Colored Jones Polynomial · It maps a diagram D of a link L to (D) e A—I] and it is characterized by the three rules: (ii) DU . The bracket polynomial is

The Temperly-Lieb Algebra

Page 28: An Introduction to The Colored Jones Polynomial · It maps a diagram D of a link L to (D) e A—I] and it is characterized by the three rules: (ii) DU . The bracket polynomial is

The Temperly-Lieb Algebra

Page 29: An Introduction to The Colored Jones Polynomial · It maps a diagram D of a link L to (D) e A—I] and it is characterized by the three rules: (ii) DU . The bracket polynomial is

The Jones-Wenzel Idempotent

Page 30: An Introduction to The Colored Jones Polynomial · It maps a diagram D of a link L to (D) e A—I] and it is characterized by the three rules: (ii) DU . The bracket polynomial is

The Jones-Wenzel Idempotent

Page 31: An Introduction to The Colored Jones Polynomial · It maps a diagram D of a link L to (D) e A—I] and it is characterized by the three rules: (ii) DU . The bracket polynomial is

The Jones-Wenzel Idempotent

Page 32: An Introduction to The Colored Jones Polynomial · It maps a diagram D of a link L to (D) e A—I] and it is characterized by the three rules: (ii) DU . The bracket polynomial is

The Colored Jones Polynomial

Page 33: An Introduction to The Colored Jones Polynomial · It maps a diagram D of a link L to (D) e A—I] and it is characterized by the three rules: (ii) DU . The bracket polynomial is

The Volume Conjecture

Page 34: An Introduction to The Colored Jones Polynomial · It maps a diagram D of a link L to (D) e A—I] and it is characterized by the three rules: (ii) DU . The bracket polynomial is

Thanks


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