Temperley Lieb recoupling theory and invariants of 3-manifolds:
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Princeton, NJ
Princeton Univ. Press
1994
|
| Series: | Annals of mathematics studies
134 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | VIII, 296 S. zahlr. graph. Darst. |
| ISBN: | 0691036411 |
Staff View
MARC
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| 245 | 1 | 0 | |a Temperley Lieb recoupling theory and invariants of 3-manifolds |c by Louis H. Kauffman and Sóstenes L. Lins |
| 246 | 1 | 3 | |a Temperley-Lieb recoupling theory and invariants of 3-manifolds |
| 264 | 1 | |a Princeton, NJ |b Princeton Univ. Press |c 1994 | |
| 300 | |a VIII, 296 S. |b zahlr. graph. Darst. | ||
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| 490 | 1 | |a Annals of mathematics studies |v 134 | |
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| 650 | 7 | |a Invariants |2 ram | |
| 650 | 7 | |a Knopentheorie |2 gtt | |
| 650 | 7 | |a Manifolds |2 gtt | |
| 650 | 7 | |a Noeuds, théorie des |2 ram | |
| 650 | 4 | |a Nuds, Théorie des | |
| 650 | 4 | |a Variétés topologiques à 3 dimensions | |
| 650 | 7 | |a Variétés topologiques à 3 dimensions |2 ram | |
| 650 | 4 | |a Invariants | |
| 650 | 4 | |a Knot theory | |
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Record in the Search Index
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| adam_text | Contents
1 Introduction 1
2 Bracket Polynomial, Temperley Lieb Algebra 5
2.1 Bracket Polynomial 5
2.2 Temperley Lieb Algebra 8
3 Jones Wenzl Projectors 13
3.1 A Standard Projector in Tn 13
3.2 The Projectors as Sums of Tangles 15
3.3 Diagrams and Structural Recursion 18
4 The 3 Vertex 22
4.1 A Special Sum of Tangles 22
4.2 A Fundamental Twist 24
4.3 Invariants of Trivalent Embedded Graphs: Pa(G) 30
4.4 The Case of P2{G) 31
5 Properties of Projectors and 3 Vertices 36
5.1 Vanishing Conditions 36
5.2 Interaction with Curls and Loops 42
6 ^ Evaluations 45
6.1 Recursive Relations 45
6.2 Shaping the Recursion 51
6.3 A Formula for the 0 nets 55
v
VI Temperley Lieb Recoupling Theory and Invariants of 3 Manifolds
7 Recoupling Theory Via Temperley Lieb Algebra 60
7.1 Recoupling Theorem 60
7.2 The case of General q 66
7.3 Orthogonality and Pentagon Identities ............ 69
8 Chromatic Evaluations and the Tetrahedron 76
8.1 Exact Formulas in a Special Case 76
8.2 Tensorial Formalism 77
8.3 A Heuristic Correspondence on the 0 Net 81
8.4 Chromatic Evaluation: General Case 83
8.5 The Tetrahedron 88
9 A Summary of Recoupling Theory 93
9.1 Bracket Polynomial 93
9.2 Temperley Lieb Algebra Tn 94
9.3 Chebyschev Polynomials 94
9.4 Quantum Integers 95
9.5 g Symmetrizer 95
9.6 Jones Wenzl Projectors 96
9.7 Curl and Projector 96
9.8 Loop and Projector 96
9.9 3 Vertex 97
9.10 0 Net 97
9.11 Tetrahedral Net 98
9.12 q 6j Symbols 99
9.13 Orthogonality Identity 99
9.14 Biedenharn Elliot (Pentagon) Identity 99
9.15 Two Special Cases 99
9.16 Axiomatics 100
10 A 3 Manifold Invariant by State Summation 102
10.1 Matveev Piergallini Moves 102
10.2 A Partition Function 104
10.3 Invariance under Lune Move 108
10.4 Invariance under the y move 109
10.5 Behavior under Bubble Move 112
Contents vii
11 The Shadow World 114
11.1 Preliminaries . 114
11.2 Shadow Translations 116
11.3 Proving Shadow World Transitions 120
11.4 Examples 125
12 The Witten Reshetikhin Turaev Invariant 129
12.1 Framed Links 129
12.2 Examples 131
12.3 Handle Sliding and Kirby Calculus 133
12.4 Consequences of Handle Slides 135
12.5 Invariants 140
12.6 Lickorish s Proof 144
12.7 Normalization 146
12.8 Gauss Sums 150
12.9 Examples 152
12.10 Shadow Interpretation 153
12.11 Appendix: Invariants of 4 Manifolds 156
13 Blinks + 3 Gems: Recognizing 3 Manifolds 160
13.1 Motivating 3 Gems 160
13.2 Graph Encoded 3 Manifolds 163
13.3 Dipole Moves: Ferri Gagliardi Theorem 167
13.4 The Sufficiency of the Matveev Piergallini Moves 168
13.5 From Blinks to 3 Gems 171
13.6 Rigid 3 Gems 175
13.7 The Code of a Bipartite (n + 1) Graph 178
13.8 TS Classes: a Basis for 3 Manifold Classification 180
14 Tables of Quantum Invariants 185
14.1 Overview of the Tables 185
14.2 Knot 3i 191
14.3 Knot 4i 205
14.4 Knot 5i 212
14.5 Knot 52 227
14.6 Knot 6i 235
14.7 Knot 62 239
14.8 Knot 63 243
Vlii Temperley Lteb Recoupling Theory and Invariants of 3 Manifolds
14.9 Knot 7i 245
14.10 Knot 72 249
14.11 Knot 73 253
14.12 Knot 74 257
14.13 Knot 75 261
14.14 Knot 76 265
14.15 Knot 77 269
14.16 Links with 2 Components 272
14.17 Links with 3 Components 286
Bibliography 290
Index 295
|
| any_adam_object | 1 |
| author | Kauffman, Louis H. 1945- Lins, Sóstenes |
| author_GND | (DE-588)134212614 |
| author_facet | Kauffman, Louis H. 1945- Lins, Sóstenes |
| author_role | aut aut |
| author_sort | Kauffman, Louis H. 1945- |
| author_variant | l h k lh lhk s l sl |
| building | Verbundindex |
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| callnumber-sort | QA 3612.2 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SI 830 SK 350 |
| classification_tum | MAT 572f |
| ctrlnum | (OCoLC)30318403 (DE-599)BVBBV009803386 |
| dewey-full | 514/.224 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 514 - Topology |
| dewey-raw | 514/.224 |
| dewey-search | 514/.224 |
| dewey-sort | 3514 3224 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
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| illustrated | Illustrated |
| indexdate | 2024-07-09T17:41:09Z |
| institution | BVB |
| isbn | 0691036411 |
| language | English |
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| physical | VIII, 296 S. zahlr. graph. Darst. |
| publishDate | 1994 |
| publishDateSearch | 1994 |
| publishDateSort | 1994 |
| publisher | Princeton Univ. Press |
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| series | Annals of mathematics studies |
| series2 | Annals of mathematics studies |
| spelling | Kauffman, Louis H. 1945- Verfasser (DE-588)134212614 aut Temperley Lieb recoupling theory and invariants of 3-manifolds by Louis H. Kauffman and Sóstenes L. Lins Temperley-Lieb recoupling theory and invariants of 3-manifolds Princeton, NJ Princeton Univ. Press 1994 VIII, 296 S. zahlr. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Annals of mathematics studies 134 Invarianten gtt Invariants Invariants ram Knopentheorie gtt Manifolds gtt Noeuds, théorie des ram Nuds, Théorie des Variétés topologiques à 3 dimensions Variétés topologiques à 3 dimensions ram Knot theory Three-manifolds (Topology) Invariante (DE-588)4128781-2 gnd rswk-swf Mannigfaltigkeit (DE-588)4037379-4 gnd rswk-swf Knotentheorie (DE-588)4164318-5 gnd rswk-swf Dimension 3 (DE-588)4321722-9 gnd rswk-swf Knoten Mathematik (DE-588)4164314-8 gnd rswk-swf Knotentheorie (DE-588)4164318-5 s DE-604 Invariante (DE-588)4128781-2 s Mannigfaltigkeit (DE-588)4037379-4 s Dimension 3 (DE-588)4321722-9 s Knoten Mathematik (DE-588)4164314-8 s Lins, Sóstenes Verfasser aut Annals of mathematics studies 134 (DE-604)BV000000991 134 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006487024&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Kauffman, Louis H. 1945- Lins, Sóstenes Temperley Lieb recoupling theory and invariants of 3-manifolds Annals of mathematics studies Invarianten gtt Invariants Invariants ram Knopentheorie gtt Manifolds gtt Noeuds, théorie des ram Nuds, Théorie des Variétés topologiques à 3 dimensions Variétés topologiques à 3 dimensions ram Knot theory Three-manifolds (Topology) Invariante (DE-588)4128781-2 gnd Mannigfaltigkeit (DE-588)4037379-4 gnd Knotentheorie (DE-588)4164318-5 gnd Dimension 3 (DE-588)4321722-9 gnd Knoten Mathematik (DE-588)4164314-8 gnd |
| subject_GND | (DE-588)4128781-2 (DE-588)4037379-4 (DE-588)4164318-5 (DE-588)4321722-9 (DE-588)4164314-8 |
| title | Temperley Lieb recoupling theory and invariants of 3-manifolds |
| title_alt | Temperley-Lieb recoupling theory and invariants of 3-manifolds |
| title_auth | Temperley Lieb recoupling theory and invariants of 3-manifolds |
| title_exact_search | Temperley Lieb recoupling theory and invariants of 3-manifolds |
| title_full | Temperley Lieb recoupling theory and invariants of 3-manifolds by Louis H. Kauffman and Sóstenes L. Lins |
| title_fullStr | Temperley Lieb recoupling theory and invariants of 3-manifolds by Louis H. Kauffman and Sóstenes L. Lins |
| title_full_unstemmed | Temperley Lieb recoupling theory and invariants of 3-manifolds by Louis H. Kauffman and Sóstenes L. Lins |
| title_short | Temperley Lieb recoupling theory and invariants of 3-manifolds |
| title_sort | temperley lieb recoupling theory and invariants of 3 manifolds |
| topic | Invarianten gtt Invariants Invariants ram Knopentheorie gtt Manifolds gtt Noeuds, théorie des ram Nuds, Théorie des Variétés topologiques à 3 dimensions Variétés topologiques à 3 dimensions ram Knot theory Three-manifolds (Topology) Invariante (DE-588)4128781-2 gnd Mannigfaltigkeit (DE-588)4037379-4 gnd Knotentheorie (DE-588)4164318-5 gnd Dimension 3 (DE-588)4321722-9 gnd Knoten Mathematik (DE-588)4164314-8 gnd |
| topic_facet | Invarianten Invariants Knopentheorie Manifolds Noeuds, théorie des Nuds, Théorie des Variétés topologiques à 3 dimensions Knot theory Three-manifolds (Topology) Invariante Mannigfaltigkeit Knotentheorie Dimension 3 Knoten Mathematik |
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