Joyce D.D. — Compact manifolds with special holonomy :: Электронная библиотека попечительского совета мехмата МГУ

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Joyce D.D. — Compact manifolds with special holonomy

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Название: Compact manifolds with special holonomy

Автор: Joyce D.D.

Аннотация:

The book starts with a thorough introduction to connections and holonomy groups, and to Riemannian, complex and Kahler geometry. Then the Calabi conjecture is proved and used to deduce the existence of compact manifolds with holonomy SU(m) (Calabi-Yau manifolds) and Sp(m) (hyperkahler manifolds). These are constructed and studied using complex algebraic geometry. The second half of the book is devoted to constructions of compact 7- and 8-manifolds with the exceptional holonomy groups 92 and Spin(7). Many new examples are given, and their Betti numbers calculated. The first known examples of these manifolds were discovered by the author in 1993-5. This is the first book to be written about them, and contains much previously unpublished material which significantly improves the original constructions.

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Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2000

Количество страниц: 447

Добавлена в каталог: 24.11.2013

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Предметный указатель

QALE manifold, radius functions      219
QALE manifold, Ricci-flat K $\ddot{a}$ hler      210—215 238—239
QALE manifold, structure group       272—278
QALE manifold, structure group Spin(7)      344—346
QALE manifold, weighted Holder space      221
QALE manifold, weighted Sobolev space      220
Quasi — ALE      see QALE manifold
Quatemionic K $\ddot{a}$ hler manifold      57 148 167—168
Quatemionic manifold      148 168—170
Quaternions      57 149
R-data      280—281 346
Reduction Theorem      31
Resolution      91
Resolution, crepant      126—132
Resolution, local product      205—207
Resolution, of $T^7/\Gamma$       282—284
Resolution, of $T^8/\Gamma$       348
Resolution, of $\mathbb{C}^m/G$       128—132
Resolution, real      236 344
Resolution, real local product      236 274 344
Resolution, small      127
Ricci curvature      44 81
Ricci curvature, and 1-forms      63—64
Ricci form      82 98 123
Riemann curvature      43—44
Riemannian holonomy      see Holonomy group
Riemannian metric      see Metric
Scalar curvature      44
Schauder estimate      14—15
Scheme      90
Schlessinger Rigidity Theorem      132
Self-dual 4-manifold      168—170
Sheaf      88—89
Sheaf, cohomology      89 93
Sheaf, invertible      126
Singularity, canonical      127
Singularity, crepant resolution      126—132
Singularity, deformation      92—93
Singularity, Kleinian      129
Singularity, nonisolated      204
Singularity, of variety      90
Singularity, resolution      91
Singularity, terminal      127 130 200
Smoothing      92 313 318 324
Sobolev embedding theorem      6 297
Sobolev space      4—5
Sobolev space, weighted      178 220
Sp() holonomy      see Hyperk $\ddot{a}$ hler manifold
Special Lagrangian submanifold      70 304 418
Spin geometry      64—68
Spin structure      65
Spin(7) holonomy      57—58 254—264
Spin(7) holonomy, Cayley 4-fold      70 267—268 371—373 417
Spin(7) holonomy, compact manifolds, Betti numbers of      370 380 385 390 416
Spin(7) holonomy, compact manifolds, constructions      360—362 395—401
Spin(7) holonomy, compact manifolds, examples      368—371 373—391 406—415
Spin(7) holonomy, compact manifolds, moduli space of      261—264
Spin(7) holonomy, compact manifolds, topology of      259—261 366—368 404—405
Spin(7) holonomy, holonomy subgroups      256
Spin(7) holonomy, metrics Ricci-flat      256

Spin(7) holonomy, parallel spinors      256
Spin(7) holonomy, research problems      416—418
Spin(7), definition      255
Spin(7)-manifold      255
Spin(7)-manifold, ALE      344 393—394
Spin(7)-manifold, product      343
Spin(7)-manifold, QALE      344—346
Spin(7)-manifold, with holonomy SU(2)      342
Spin(7)-manifold, with holonomy SU(3), etc.      343
Spin(7)-orbifolds $Y/(\sigma)$       395—396
Spin(7)-orbifolds $Y/(\sigma)$ , examples      406—415
Spin(7)-orbifolds $Y/(\sigma)$ , resolutions      398
Spin(7)-orbirolds $T^8/\Gamma$       346—347
Spin(7)-orbirolds $T^8/\Gamma$ , examples      369 373 381 386
Spin(7)-orbirolds $T^8/\Gamma$ , R-data      346
Spin(7)-orbirolds $T^8/\Gamma$ , resolutions      348
Spin(7)-structure      255
Spin(7)-structure, admissible 4-form      255
Spin(7)-structure, function $\Theta$       257—258
Spin(7)-structure, small torsion      355 398
Spin(7)-structure, splitting of forms      256 260
Spin(7)-structure, torsion      255
Spin(7)-structure, torsion-free      255
Spinor      65
Spinor, harmonic      67
Spinor, parallel      66 245 256
Stokes’ Theorem      2
String theory      144—146
SU() holonomy      see Calabi — Yau manifold
Symmetric space      50—55
Symmetric space, constant curvature      54
Symmetric space, definition      50
Torelli Theorem, Global      158 164
Torelli Theorem, Local      158 163
Torelli Theorem, Weak      158
Toric geometry      129
Torsion      35—36
Torsion of -structure      40
Twistor space      151—152 168 169
Variety      86—90
Variety, abstract      89
Variety, affine      87
Variety, algebraic      74—75 87
Variety, analytic      90
Variety, blowing up      91—92
Variety, deformation      92—93
Variety, morphism      88
Variety, projective      87
Variety, rational map      88
Variety, resolution      91
Variety, singular      90
Variety, toric      129
Vector bundle      20
Vector bundle, connection      22
Vector bundle, holomorphic      77
Vector bundle, line bundle      see Line bundle
Weighted projective space      133 140 401
Weitzenbock formula      61 125
Weyl group      154—155 241
Wolf space      168
Zariski topology      86 87

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