Kerler Th., Lyubashenko V.V. — N on-Semisimple Topological Quantum Field Theories for 3-Manifolds with Corners :: Электронная библиотека попечительского совета мехмата МГУ

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Kerler Th., Lyubashenko V.V. — N on-Semisimple Topological Quantum Field Theories for 3-Manifolds with Corners

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Название: N on-Semisimple Topological Quantum Field Theories for 3-Manifolds with Corners

Авторы: Kerler Th., Lyubashenko V.V.

Аннотация:

This book presents the (to date) most general approach to combinatorial constructions of topological quantum field theories (TQFTs) in three dimensions. The authors describe extended TQFTs as double functors between two naturally defined double categories: one of topological nature, made of 3-manifolds with corners, the other of algebraic nature, made of linear categories, functors, vector spaces and maps. Atiyah's conventional notion of TQFTs as well as the notion of modular functor from axiomatic conformal field theory are unified in this concept. A large class of such extended modular catergory is constructed, assigning a double functor to every abelian modular category, which does not have to be semisimple.

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2001

Количество страниц: 379

Добавлена в каталог: 17.08.2008

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Предметный указатель

$Cob_2^{cn}$       18
$COB_{2}$       18 20
$e_{j}^{k+1}$       51
$M_{0}$       70
$o_{h}$       5 343
$o_{v}$       5 343
$TS1^{\spadesuit}-TS3^{\spadesuit}$ Moves      145
$\alpha$       21
$\beta$ -Move      148
$\bigotimes_{op}$       220
$\Delta$ , comultiplication      226 272
$\Delta$ , map $\widetilde{COB} \longrightarrow$ Cob      74
$\gamma$       226
$\int^{X\epsilonC}$       262
$\int_{H}, _{H}\int, \int^{H}, ^{H}\int$       229
$\kappa$ -Move      152
$\langle M_{0} \rangle$       71
$\mathbb{F}$       270
$\mathbf{AbCat}$       4 243
$\mathbf{c}$       222
$\mathbf{Inc}^+$       166
$\mathbf{Isl}^+$       167
$\mathbf{k}$       2 8 268
$\mathbf{l}$       218
$\mathbf{R}$       218
$\mathbf{u}_{0}^2$       223
$\mathbf{u}_{0}^4$       223
$\mathbf{u}_{1}^2$       223
$\mathbf{V-Cat-mod}$       249
$\mathbf{V-Cat^r}$       248
$\mathbf{V-Cat}$       247
$\mathbf{V^A}$       248
$\mathbf{V}$       246
$\mathbf{V}$ -category      246
$\mathbf{V}$ -functor      247
$\mathbf{V}$ -natural transformation      247
$\mathbf{\sum}$       20
$\mathbf{\sum}_{S_{q}}$       23 33
$\mathbf{\tau}$       188
$\mathcal{D}iff^+$       36
$\mathcal{E}mbd^+$       40
$\mathcal{F}$       296
$\mathcal{F}^C$       188
$\mathcal{F}^{0}$       189
$\mathcal{F}_{\alpha}^1$       189
$\mathcal{F}_{\beta}^1$       189
$\mathcal{F}_{\gamma}^1$       191
$\mathcal{H}_g^+$       70
$\mathcal{H}_g^-$       70
$\mathcal{H}_{g_{sc}}^{g_{tg}}$       71
$\mathcal{MPTT}$       357
$\mathcal{M} (g, a/b)$       40
$\mathcal{O}_{1}$ -Move      115
$\mathcal{O}_{2}$ -Move      150
$\mathcal{O}_{3}$ -Move      148
$\mathcal{PTG}$       357
$\mathcal{PTT}$       353
$\mathcal{Tgl}$       116
$\mathcal{T}gl^{tg1\longrightarrow\infty}$       168
$\mathcal{T}gl_{S^2}$       137
$\mathcal{T}gl_{S^2}^{Ki}$       150
$\mathcal{T}gl_{S^2}^{nx}$       138
$\mathcal{T}gl_{S^2}^{s;*}$       139
$\mathcal{T}gl_{S^2}^{\mathbf{BL}}$       144
$\mathcal{T}gl_{S^2}^{\mathbf{FR}}$       152
$\mathcal{T}gl_{\mathbb{R}^2}$       118
$\mathcal{T}gl_{\mathbb{R}^2}^{dec-proj}$       123
$\mathcal{T}gl_{\mathbb{R}^2}^{plan}$       125
$\mathcal{T}gl_{\mathbb{R}^2}^{well-pos}$       119
$\mathcal{UPTG}$       362
$\mathfrak{G_{urg2}}$       199 204 206 207 211
$\mathfrak{G_{urg}}$       11 773
$\mu$       279 331
$\Psi$       23
$\sigma$ -Move      151
$\Upsilon$       22 157
$\widehat{B_{b}}$       40
$\widehat{\mathcal{P}_{b}}$       40
$\widetilde{COB}$       68 73 76
$_{[1,2]} \mathcal{F}^0$       191
$_{[1,2]} \mathcal{F}^1$       191
1-2-cancellation      114
1-2-Slide      197
1-Handle Slide      197
2-category      344
2-framing      69
2-Handle Slide      150
Admissible tangle      108
Admissible tangle in $S^{1} \times [-1, 1]$       136
Admissible tangle, embedded      117
Antipode      226 274
arc-diagram      314
Associativity constraint      218
Balanced category      223
Beak Lemma      190
Birth point      189
Bounded category      8 218 243
Braided category      222
Braiding      222
Bridged link      57
Bridged link diagram      202
Category with split idempotents      229
CFT      3
CFT, Segal's axioms      336
Chern — Simons theory      3 335
Cob      24 26
Cob(a, b)      24
Cobordant      75
Cobordism      2
Cobordism group      76
Coend      262
Coend $\mathbb{F}$       270
Coend F      270
coev      219
Coevaluation      219

Colored surface      294
Coloring      286
Connecting Annulus Move      149
Critical manifold      190
Death point      189
Deligne's tensor product      243 259
Dinatural transformation      262
Double category      4 343
Double functor      345
Dovetail Lemma      190
Dual Hopf algebra      227
Essentially small category      4 270
EV      219
Evaluation      219
Fenn — Rourke Move      152
Fill functor      30 74
Framed braid group      40
Frobenius algebra      19
General Cancellation Move      149
Handle      51
Handle decomposition      53
Handle decomposition, generic      53
Handle trading      113 177
Handlebody      38 70
Hennings invariant      332
Hopf algebra      226
Hopf pairing      227
Hopf — Link Move      150
Horizontal 1-morphism (1-arrow)      4 343
Horizontal composition      5 343
Horizontal composition in $\mathcal{T}gl$       156
Horizontal composition in $\widetilde{\mathbf{COB}}$       78
Horizontal transformation      351
Horizontal transformation, modification      352
Independent Trajectories Principle      190
Int H      229
Integral-element      229 279
Integral-functional      229 280
Interchange law      5 343
Interval, auxiliary      101
Interval, external      101
Interval, internal      101
Karoubi enveloping category      229
Mapping class group      36—38
Mapping class group, stable      38
Marked Planar Thick Tangles      357
Modular category      8 276
Monoidal 2-category, braided semistrict      257
Monoidal 2-category, semistrict      245 249
Monoidal 2-category, symmetric      257 259
Monoidal category      218
Monoidal functor      219
Morphism of monoidal functor      219
Morse function      51
Object of integrals      230
Planar Thick Graphs      357
Planar Thick Tangles      353
Pseudofunctor      345
Pure braid group      40
Quintet      5 344
Recombination functor      32
Reidemeister moves      110 129
Relative cobordism      4
Reshetikhin — Turaev invariant      10 320
Ribbon auxiliary      102
Ribbon bottom      106
Ribbon category      224
Ribbon category, strictly rigid      224
Ribbon closed      105
Ribbon external      102
Ribbon Hopf algebra      330
Ribbon internal      102
Ribbon through      106
Ribbon top      105
Ribbon twist      223
Ribbon-TS3 Move      151
Rigid category      219
Self-dual Hopf algebra      228
Side-invertible      232
Signature      69
Signature Cancellation Move      152
Smale cancellation      54
Split idempotent      229
Splitting functor      32
Standard closure      71
Standard connected cobordism      71
Standard handlebody      70 84
Standard surface      6 20
Surgery      52
Surgery balls      144
Surgery ribbons      94 200
Surgery, Dehn      56
TD1-TD5 Moves      112—113
TD3**-TD5** Moves      318
TD3*-TD5* Moves      140
Tensor product      218
Tgl      116
TI1-TI11 Moves      110—112
TQFT      283
TQFT, Atiyah's axioms      1
TQFT, enhanced      315
TQFT, extended      7
Triangle Lemma      190
TS1**-TS3** Moves      318
TS1*-TS3* Moves      140—141
TS1-TS5 Moves      113—115
Unit object      218
Useful Planar Thick Graphs      362
Verlinde formula      322
Vertical 1-morphism (1-arrow)      4 343
Vertical composition      5 343
Vertical composition in $\mathcal{T}gl$       155
Vertical composition in $\widetilde{\mathbf{COB}}$       76
Wall cocycle      77
Well-positioned tangle      119
Wilson lines      6 336

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