Frobenius algebras and 2D topological quantum field theories:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cambridge [u.a.]
Cambridge Univ. Press
2004
|
| Ausgabe: | 1. publ. |
| Schriftenreihe: | London Mathematical Society student texts
59 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XIII, 240 S. Ill., graph. Darst. |
| ISBN: | 9780521832670 0521832675 9780521540315 0521540313 |
Internformat
MARC
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| 100 | 1 | |a Kock, Joachim |e Verfasser |0 (DE-588)132344653 |4 aut | |
| 245 | 1 | 0 | |a Frobenius algebras and 2D topological quantum field theories |c Joachim Kock |
| 250 | |a 1. publ. | ||
| 264 | 1 | |a Cambridge [u.a.] |b Cambridge Univ. Press |c 2004 | |
| 300 | |a XIII, 240 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a London Mathematical Society student texts |v 59 | |
| 650 | 7 | |a Algebraïsche structuren |2 gtt | |
| 650 | 4 | |a Champs, Théorie quantique des | |
| 650 | 4 | |a Corps topologiques | |
| 650 | 4 | |a Frobenius, Algèbres de | |
| 650 | 7 | |a Kwantumveldentheorie |2 gtt | |
| 650 | 4 | |a Frobenius algebras | |
| 650 | 4 | |a Quantum field theory | |
| 650 | 4 | |a Topological fields | |
| 650 | 0 | 7 | |a Topologische Quantenfeldtheorie |0 (DE-588)4426450-1 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Frobenius-Algebra |0 (DE-588)4155476-0 |2 gnd |9 rswk-swf |
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| 689 | 0 | 1 | |a Topologische Quantenfeldtheorie |0 (DE-588)4426450-1 |D s |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-012961584 | ||
Datensatz im Suchindex
| _version_ | 1804133001292939264 |
|---|---|
| adam_text | Contents
Preface
page vii
General conventions
xiv
Introduction
1
1
Cobordisms and topological quantum field theories
9
Summary
9
1.1
Geometric preliminaries
10
Manifolds with boundary
10
Orientations
12
Some vocabulary from Morse theory
15
1.2
Cobordisms
18
Unoriented cobordisms
18
Oriented cobordisms
22
Decomposition of cobordisms
28
Topological quantum field theories
30
1.3
The category of cobordism classes
34
Gluing and composition
35
Identity cobordisms and invertible cobordisms
44
Monoidal structure
48
Topological quantum field theories
54
1.4
Generators and relations for 2Cob
56
Preliminary observations
56
Generators
62
Relations
69
Relations involving the twist
72
Sufficiency of the relations
73
2
Frobenius algebras
78
Summary
78
xi
xii Contents
2.1
2.2
2.3
2.4
3.1
3.2
3.3
3.4
3.5
Algebraic preliminaries
79
Vector spaces, duals, and pairings
79
Algebras and modules
86
Definition and examples of Frobenius algebras
94
Definition and basic properties
94
Examples
98
Frobenius algebras and comultiplication
106
Graphical calculus
108
Commutativity and cocommutativity
121
Tensor calculus (linear algebra in coordinates)
123
The category of Frobenius algebras
131
Frobenius algebra homomorphisms
131
Tensor products of Frobenius algebras
132
Digression on bialgebras
135
Monoids and monoidal categories
138
Summary
138
Monoids (in Set)
139
Some notions from set theory
139
Definition of monoid
140
Examples
143
Monoid actions and representations
146
Monoidal categories
148
Definition of monoidal categories
150
Nonstrict monoidal categories
154
Examples of monoidal categories and functors
157
Symmetric monoidal categories
160
Monoidal functor categories
167
Frobenius algebras and 2-dimensional topological
quantum field theories
171
The simplex categories
Δ
and
Φ
177
Finite ordinals
177
Graphical description of
Δ
180
Generators and relations for
Δ
183
The symmetric equivalent: finite cardinals
188
Generators and relations for
Φ
192
Monoids in monoidal categories, and monoidal
functors from
Δ
197
Monoids in monoidal categories
197
Examples
201
Monoidal functors from the simplex category
204
Contents
Algebras
207
Symmetrie monoidal
functors on
Φ
208
3.6
Frobenius structures
212
Comonoids and
coalgebras
212
Frobenius objects, Frobenius algebras,
and 2-dimensional cobordisms
214
Appendix: vocabulary from category theory
223
A.I Categories
223
A.2 Functors
226
A.3 Universal objects
230
References
234
index
237
|
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| discipline | Physik Mathematik |
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| illustrated | Illustrated |
| indexdate | 2024-07-09T20:01:46Z |
| institution | BVB |
| isbn | 9780521832670 0521832675 9780521540315 0521540313 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-012961584 |
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| physical | XIII, 240 S. Ill., graph. Darst. |
| publishDate | 2004 |
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| series | London Mathematical Society student texts |
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| spelling | Kock, Joachim Verfasser (DE-588)132344653 aut Frobenius algebras and 2D topological quantum field theories Joachim Kock 1. publ. Cambridge [u.a.] Cambridge Univ. Press 2004 XIII, 240 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier London Mathematical Society student texts 59 Algebraïsche structuren gtt Champs, Théorie quantique des Corps topologiques Frobenius, Algèbres de Kwantumveldentheorie gtt Frobenius algebras Quantum field theory Topological fields Topologische Quantenfeldtheorie (DE-588)4426450-1 gnd rswk-swf Frobenius-Algebra (DE-588)4155476-0 gnd rswk-swf Frobenius-Algebra (DE-588)4155476-0 s Topologische Quantenfeldtheorie (DE-588)4426450-1 s b DE-604 London Mathematical Society student texts 59 (DE-604)BV000841726 59 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=012961584&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Kock, Joachim Frobenius algebras and 2D topological quantum field theories London Mathematical Society student texts Algebraïsche structuren gtt Champs, Théorie quantique des Corps topologiques Frobenius, Algèbres de Kwantumveldentheorie gtt Frobenius algebras Quantum field theory Topological fields Topologische Quantenfeldtheorie (DE-588)4426450-1 gnd Frobenius-Algebra (DE-588)4155476-0 gnd |
| subject_GND | (DE-588)4426450-1 (DE-588)4155476-0 |
| title | Frobenius algebras and 2D topological quantum field theories |
| title_auth | Frobenius algebras and 2D topological quantum field theories |
| title_exact_search | Frobenius algebras and 2D topological quantum field theories |
| title_full | Frobenius algebras and 2D topological quantum field theories Joachim Kock |
| title_fullStr | Frobenius algebras and 2D topological quantum field theories Joachim Kock |
| title_full_unstemmed | Frobenius algebras and 2D topological quantum field theories Joachim Kock |
| title_short | Frobenius algebras and 2D topological quantum field theories |
| title_sort | frobenius algebras and 2d topological quantum field theories |
| topic | Algebraïsche structuren gtt Champs, Théorie quantique des Corps topologiques Frobenius, Algèbres de Kwantumveldentheorie gtt Frobenius algebras Quantum field theory Topological fields Topologische Quantenfeldtheorie (DE-588)4426450-1 gnd Frobenius-Algebra (DE-588)4155476-0 gnd |
| topic_facet | Algebraïsche structuren Champs, Théorie quantique des Corps topologiques Frobenius, Algèbres de Kwantumveldentheorie Frobenius algebras Quantum field theory Topological fields Topologische Quantenfeldtheorie Frobenius-Algebra |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=012961584&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000841726 |
| work_keys_str_mv | AT kockjoachim frobeniusalgebrasand2dtopologicalquantumfieldtheories |