Non-semisimple topological quantum field theories for 3-manifolds with corners:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin ; Heidelberg ; New York ; Barcelona ; Hong Kong ; London
Springer
2001
|
| Series: | Lecture notes in mathematics
1765 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | VI, 379 S. graph. Darst. |
| ISBN: | 3540424164 |
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MARC
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| 245 | 1 | 0 | |a Non-semisimple topological quantum field theories for 3-manifolds with corners |c Thomas Kerler ; Volodymyr V. Lyubashenko |
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Record in the Search Index
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| adam_text | Contents
0. Introduction and Summary of Results 1
0.1 Atiyah s TQFT Axioms via Categories 1
0.2 Double Categories 3
0.3 Extended TQFT s 6
0.4 Statement of Main Result on the Class of Extended TQFT s 8
1. The Double Category of Framed, Relative 3 Cobordisms 15
1.1 The 0 1 Arrow Category of Surfaces with Boundaries 18
1.2 2 Arrows from Cobordisms with Corners 23
1.3 Basic Consequences of the Double Category Picture 27
1.4 Mapping Class Groups, Framed Braid Groups, and Balancing 35
1.5 Some Facts about Handle Decompositions 51
1.6 The Central Extension i?4 Cob + Cob 68
2. Tangle Categories and Presentation of Cobordisms 97
2.1 Local Ingredients of Tangle Diagrams and Horizontal 1 Arrows ... 99
2.2 Admissible Tangles and Vertical 1 Arrows 104
2.3 Equivalence Moves of Tangles, and the 2 Arrows in Tgl 109
2.4 Tangles in Three Space 116
2.5 Alternative Calculi and Further Equivalences 143
2.6 Compositions and Tgl as a Double Category 153
2.7 Special Cases and Applications 166
3. Isomorphism between Tangle and Cobordism Categories 173
3.1 Trading and Eliminating Handles 175
3.2 Stratified Function Spaces and External Strands onW 187
3.3 From Tangle Classes to Cobordism Classes 199
3.4 Verification of Compositions 207
4. Monoidal categories and monoidal 2 categories 217
4.1 Ribbon monoidal categories 217
4.2 Hopf algebras in braided categories 226
4.3 Abelian categories form a monoidal 2 category 242
VI Contents
5. Coends and construction of Hopf algebras 261
5.1 Thecoend 261
5.2 Braided function algebra 270
6. Construction of TQFT Double Functors 283
6.1 Main result 283
6.2 Colorations, Natural Transformations, and Liftings 284
6.3 Topological Invariance 290
6.4 Compositions over Colored Surfaces 292
6.5 Lifting V(M) to Color Independent Natural Transformation 294
6.6 Horizontal Compositions 299
6.7 Topological moves imply the modularity 304
7. Generalization of a modular functor 313
7.1 Enhanced cobordism categories 313
7.2 Formulation of TQFT as a double functor in the extended case 315
7.3 Sketch of the construction of enhanced TQFT 315
7.4 Examples 320
A. From Quantum Field Theory to Axiomatics 335
A.I Witten Chern Simons Theory and Conformal Field Theory 335
A.2 Developing the Axiomatics for Extended TQFT s 338
A.3 Generalized TQFT s in Gauge Theory 341
B. Double Categories and Double Functors 343
B.I Double Categories 343
B.2 Double pseudofunctors 345
C. Thick tangles 353
C.I Monoidal bicategory of thick tangles 353
C.2 Representation of thick tangles by abelian categories 365
Index 377
|
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| author | Kerler, Thomas Ljubašenko, Volodymyr 1959- |
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| indexdate | 2024-07-09T18:53:12Z |
| institution | BVB |
| isbn | 3540424164 |
| language | English |
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| series2 | Lecture notes in mathematics |
| spelling | Kerler, Thomas Verfasser aut Non-semisimple topological quantum field theories for 3-manifolds with corners Thomas Kerler ; Volodymyr V. Lyubashenko Berlin ; Heidelberg ; New York ; Barcelona ; Hong Kong ; London Springer 2001 VI, 379 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Lecture notes in mathematics 1765 Topologische Quantenfeldtheorie - Kategorientheorie Mathematische Physik Mathematical physics Quantum field theory Three-manifolds (Topology) Kategorientheorie (DE-588)4120552-2 gnd rswk-swf Topologische Quantenfeldtheorie (DE-588)4426450-1 gnd rswk-swf Topologische Quantenfeldtheorie (DE-588)4426450-1 s Kategorientheorie (DE-588)4120552-2 s DE-604 Ljubašenko, Volodymyr 1959- Verfasser (DE-588)123063124 aut Lecture notes in mathematics 1765 (DE-604)BV000676446 1765 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009475352&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Kerler, Thomas Ljubašenko, Volodymyr 1959- Non-semisimple topological quantum field theories for 3-manifolds with corners Lecture notes in mathematics Topologische Quantenfeldtheorie - Kategorientheorie Mathematische Physik Mathematical physics Quantum field theory Three-manifolds (Topology) Kategorientheorie (DE-588)4120552-2 gnd Topologische Quantenfeldtheorie (DE-588)4426450-1 gnd |
| subject_GND | (DE-588)4120552-2 (DE-588)4426450-1 |
| title | Non-semisimple topological quantum field theories for 3-manifolds with corners |
| title_auth | Non-semisimple topological quantum field theories for 3-manifolds with corners |
| title_exact_search | Non-semisimple topological quantum field theories for 3-manifolds with corners |
| title_full | Non-semisimple topological quantum field theories for 3-manifolds with corners Thomas Kerler ; Volodymyr V. Lyubashenko |
| title_fullStr | Non-semisimple topological quantum field theories for 3-manifolds with corners Thomas Kerler ; Volodymyr V. Lyubashenko |
| title_full_unstemmed | Non-semisimple topological quantum field theories for 3-manifolds with corners Thomas Kerler ; Volodymyr V. Lyubashenko |
| title_short | Non-semisimple topological quantum field theories for 3-manifolds with corners |
| title_sort | non semisimple topological quantum field theories for 3 manifolds with corners |
| topic | Topologische Quantenfeldtheorie - Kategorientheorie Mathematische Physik Mathematical physics Quantum field theory Three-manifolds (Topology) Kategorientheorie (DE-588)4120552-2 gnd Topologische Quantenfeldtheorie (DE-588)4426450-1 gnd |
| topic_facet | Topologische Quantenfeldtheorie - Kategorientheorie Mathematische Physik Mathematical physics Quantum field theory Three-manifolds (Topology) Kategorientheorie Topologische Quantenfeldtheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009475352&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000676446 |
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