CONTENTS i * 5.4. Bura u an d Gassne r representations 4 8 5.5. Representation s i n the e x algebras 5 0 5.6. Representation s i n the Pimsner-Popa-Temperley-Lieb algebr a (PPTL) 5 2 5.7. QIS M representations o f the braid group 5 3 5.8. Th e Potts model and Gaussia n representation s 5 5 5.9. Mor e representations 5 6 Lecture 6. Knot s and Links 5 9 6.1. Knot s and links 5 9 6.2. Th e fundamental grou p and th e Alexander module 6 0 6.3. Seifer t surface s 6 2 6.4. Seifer t matrices , S-equivalence 6 3 6.5. Untwiste d double s of knots have trivial Alexander modul e . . . . 6 5 6.6. Skei n relation for th e Alexander polynomia l 6 6 6.7. Close d braids and the Bura u representatio n 6 7 Lecture 7. Th e Knot Polynomial V L 6 9 7.1. Firs t definitio n o f V L 6 9 7.2. Th e theory of plats 7 0 7.3. A second definition o f V L , the plat approach 7 1 7.4. Kauffman' s e, - diagrammatics 7 2 7.5. Skei n relation, third definitio n o f V L 7 3 7.6. Th e skein polynomial, inductiv e definition 7 4 7.7. Th e Kauffman polynomia l 7 5 7.8. Kauffman' s "state s model", fourth an d best definition o f V L . . . 7 6 Lecture 8. Knot s and Statistical Mechanics 7 9 8.1. Statistica l mechanic s formalis m 7 9
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