Sossinsky:Knots. Mathematics with a twist.pdf - English

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CONTENTS PREFACE vii 1. ATOMS AND KNOTS 1 Lord Kelvin • 1860 2. BRAIDED KNOTS 1S Alexander • 1923 3. PLANAR DIAGRAMS OF KNOTS 3S Reidemeister • 1928 4. THE ARITHMETIC OF KNOTS 46 Schubert • 1949 5. SURG ERY AND INVARIANTS S8 Conway • 1973 6. JONES'S POLYNOMIAL AND SPIN MODELS 73 Ka uffman • 1987 7. FINITE-ORDER INVARIANTS 90 Vassiliev • 1990 8. KNOTS AND PHYSICS 10S Xxx? • 2004? NOTES 121 WORKS CITED 127
Page 2 and 3: ALEXEI SOSSINSKY TRANSLATED BY CIS
Page 6 and 7: PREFA CE Butterfly knot, dover hitc
Page 8 and 9: PREFACE ix Readers will also have t
Page 10 and 11: (a) li PREFACE xi Figure P.l. Some
Page 12 and 13: PREFACE Strand (Iine) Figure P.4. A
Page 14 and 15: PREFACE xv To end this overview of
Page 16 and 17: PREFACE XVII 1949 by the German Hor
Page 18: PREFACE XIX cians, whose only motiv
Page 22 and 23: I ATOMS ANO KNOTS (Lord Kelvin· 18
Page 24 and 25: ATO MS ANO KNOTS Figure 1.2. Three
Page 26 and 27: ATO MS ANO KNOTS 5 Figure 1.4. Two
Page 28 and 29: ATO MS ANO KNOTS 7 %%%%% Figure 1.6
Page 30 and 31: ATO MS ANO KNOTS Figure 1.7. A knot
Page 32 and 33: ATO MS AND KNOTS 11 then the four (
Page 34 and 35: ATO MS AND KNOTS 13 blindo But actu
Page 36 and 37: BRAIDED KNOTS (Alexander· 1923) Th
Page 38 and 39: BRAIDED KNOTS 17 %%%%%%%%\h:\h::'.\
Page 40 and 41: BRAI DED KNOTS 19 Figure 2.4. Unrol
Page 42 and 43: BRAIDED KNOTS 21 Figure 2.6. Desing
Page 44 and 45: BRAI DED KNOTS 23 %%%%%%%% (a) (b)
Page 46 and 47: BRAIDED KNOTS 2S est Seifert circle
Page 48 and 49: BRAI DED KNOTS 27 (a) (b) (c) Figur
Page 50 and 51: BRAIDED KNOTS 29 braid obtained by
Page 52 and 53: BRAI DED KNOTS i i+l i+ 2 i+l i+ 2
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BRAIDED KNOTS 33 Iation, which take
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3 PLANAR DIAGRAMS OF KNOTS (Reideme
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PLANAR DIAGRAMS OF KNOTS 37 (a) (b)
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PLANAR DIAGRAMS OF KNOTS 39 single
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PLANAR DIAGRAMS OF KNOTS 41 If one
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PLANAR DIAGRAMS OF KNOTS 43 This ot
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PLANAR DIAGRAMS OF KNOTS 45 rithm (
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THE ARITHMETIC OF KNOTS 47 - C Y F
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THE ARITHMETIC OF KNOTS 49 a#b= b#a
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TH E ARITHMETIC OF KNOTS 51 cause o
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TH E ARITHMETIC OF KNOTS 53 just co
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THE ARITH METI C OF KNOTS 55 ber l
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TH E ARITHMETIC OF KNOTS 57 added;
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SURGERY ANO INVA RIANTS 59 %%%%%%%%
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SURGERY AND INVA RIANTS 61 Figure 5
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SURGERY AN D INVA RIANTS 63 the enz
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SURGERY AND INVA RIANTS 65 Figure 5
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SURGERY AND INVARIANTS 67 Invarianc
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SURGERY AND INVA RIANTS 69 FinalIy,
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SURGERY AND INVA RIANTS 71 tion sim
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6 JONES'S POLYNOMIAL AN O SPIN MOOE
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JONES'S POLYNOMIAL AND SPIN MODELS
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JONES'S POLYNOMIAL ANO SPIN MOOELS
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Page 102 and 103:
JONES'S POLYN OMIAL AND SPIN MODELS
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Page 106 and 107:
Page 108 and 109:
Page 110 and 111:
Page 112:
FI NITE-ORDER INVARIANTS 91 when on
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94 KNOTS yes, both in this particul
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96 KN OTS A Brief Description of th
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98 KNOTS Actually, deducing equatio
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100 KNOTS who like these things can
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102 KNOTS and I have not drawn the
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104 KNOTS nonequivalent knots can h
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106 KNOTS to me that there is. I am
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108 KNOTS abled him to describe the
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110 KNOTS global parameters of the
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112 KNOTS easily to the most famous
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114 KNOTS ampIe is shown in Figure
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116 KNOTS . . .. . .. 0 O . . .
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118 KNOTS Jacobi identity to constr
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Preface NOTES l. For those who know
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NOTES 123 (since it hasn't succeede
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NOTES 125 we have not shown anythin
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WO RKS CITED Adams, C. 1994. The Kn
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