The Link Invariants of the Chern-Simons Field Theory: New Developments in Topological Quantum Field Theory

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Walter de Gruyter, Jan 1, 1993 - Mathematics - 326 pages
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Editorial Board

Lev Birbrair, Universidade Federal do Ceará, Fortaleza, Brasil
Victor P. Maslov, Russian Academy of Sciences, Moscow, Russia
Walter D. Neumann, Columbia University, New York, USA
Markus J. Pflaum, University of Colorado, Boulder, USA
Dierk Schleicher, Jacobs University, Bremen, Germany

 

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Contents

138 Connected sums
153
139 Mutations
156
Chapter 14 Unitary groups
161
142 Casimir operator
164
143 Composite states
168
144 Pattern links
172
145 Higher dimensional representations
176
146 Polynomial structure
179

Chapter 4 NonAbelian ChernSimons theory
31
42 Oneloop effective action
34
43 Higher order results
39
Chapter 5 Observables and perturbation theory
42
52 Perturbative computations
44
Chapter 6 Properties of the expectation values
47
62 Discrete symmetries
49
63 Satellite formulae
50
Chapter 7 Ordering fermions and knot observables
58
72 Antiperiodic boundary conditions
60
73 Knot observables
64
Chapter 8 Braid group
66
82 Hecke algebra
69
Chapter 9 Rmatrix and braids
74
92 Lie algebras and monodromy representations
79
93 QuasiHopf algebra
80
Chapter 10 ChernSimons monodromies
83
102 Universality of the link invariants
87
103 The inexistent shift
90
Chapter 11 Defining relations
92
Chapter 12 The extended Jones polynomial
102
122 Hopf link
108
123 Trefoil knot
110
124 Figureeight knot
112
125 Connection with the Jones polynomial
118
126 Bracket connection
120
127 Reconstruction theorems
122
Chapter 13 General properties
127
132 Recovered field theory
130
133 Links in a solid torus
133
134 Satellites
138
135 Skein relation
141
136 Projectors
145
137 Borromean rings
147
147 SU3 examples
181
Chapter 15 Reduced tensor algebra
187
152 Outlook
190
153 Representation ring
192
154 The threesphere
195
155 Reduced tensor algebra
196
156 Roots of unity
201
157 Special cases
204
Chapter 16 Surgery on threemanifolds
208
162 Solid tori
209
163 Dehn surgery
214
164 Links in threemanifolds
217
165 Elementary surgeries
220
166 Physical interpretation
222
167 The fundamental group
224
Chapter 17 Surgery and field theory
228
172 Properties of the Hopf matrix
231
173 Elementary surgery operators
237
174 Surgery operator
243
175 Surgery rules and Kirby moves
246
Chapter 18 Observables in threemanifolds
249
182 The manifold RP3
258
183 Lens spaces
262
184 The Poincaré manifold
266
185 The manifold T2 S1
269
Chapter 19 Threemanifold invariant
272
192 Values of the invariant
278
Chapter 20 Abelian surgery invariant
283
202 Abelian surgery rules
289
203 Abelian surgery invariant
292
References
303
Subject Index
311
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