√лавна€    Ex Libris     ниги    ∆урналы    —татьи    —ерии     аталог    Wanted    «агрузка    ’удЋит    —правка    ѕоиск по индексам    ѕоиск    ‘орум   
blank
јвторизаци€

       
blank
ѕоиск по указател€м

blank
blank
blank
 расота
blank
Joyce D.D. Ч Compact manifolds with special holonomy
Joyce D.D. Ч Compact manifolds with special holonomy

„итать книгу
бесплатно

—качать книгу с нашего сайта нельз€

ќбсудите книгу на научном форуме



Ќашли опечатку?
¬ыделите ее мышкой и нажмите Ctrl+Enter


Ќазвание: Compact manifolds with special holonomy

јвтор: Joyce D.D.

јннотаци€:

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 This is the first book to be written about them, and contains much previously unpublished material which significantly improves the original constructions.


язык: en

–убрика: ћатематика/

—татус предметного указател€: √отов указатель с номерами страниц

ed2k: ed2k stats

√од издани€: 2000

 оличество страниц: 447

ƒобавлена в каталог: 24.11.2013

ќперации: ѕоложить на полку | —копировать ссылку дл€ форума | —копировать ID
blank
ѕредметный указатель
$*$      see Hodge star
$C^{k,\alpha}(M)$      see H$\ddot{o}$lder space
$C^{k}$ space      5
$G$-structure      38
$G_2$-manifold      243
$G_2$-manifold, product      274
$G_2$-manifold, QALE      272Ч278
$G_2$-manifold, with holonomy SU(2)      271
$G_2$-manifold, with holonomy SU(3)      272
$G_2$-orbifolds $T^7 / \Gamma$      278Ч280
$G_2$-orbifolds $T^7 / \Gamma$, examples      312 315 316 329 334Ч337
$G_2$-orbifolds $T^7 / \Gamma$, R-data      280Ч281
$G_2$-orbifolds $T^7 / \Gamma$, resolutions of $T^7 / \Gamma$      282Ч284
$G_2$-structure      243
$G_2$-structure, function $\Theta$      243 249
$G_2$-structure, nearly parallel      269
$G_2$-structure, positive 3-form      243
$G_2$-structure, positive 4-form      243
$G_2$-structure, small torsion      284 286
$G_2$-structure, splitting of forms      244 245
$G_2$-structure, torsion      243
$G_2$-structure, torsion-free      243
$G_{2}$ holonomy      57Ч58 242Ч254
$G_{2}$ holonomy, associative 3-fold      70 264Ч265 326Ч327 417
$G_{2}$ holonomy, coassociative 4-fold      70 265Ч267 327Ч328 417
$G_{2}$ holonomy, compact manifolds, Betti numbers of      314 315 323 325 326 332Ч334 339
$G_{2}$ holonomy, compact manifolds, constructions      294Ч295 303Ч305
$G_{2}$ holonomy, compact manifolds, examples      309Ч326 329Ч338
$G_{2}$ holonomy, compact manifolds, finding $\pi_{1} (M)$      307Ч308
$G_{2}$ holonomy, compact manifolds, finding Betti numbers      308Ч309
$G_{2}$ holonomy, compact manifolds, moduli space of      251Ч254
$G_{2}$ holonomy, compact manifolds, topology of      245Ч247 306Ч309
$G_{2}$ holonomy, compact manifolds, with $\pi_{1}(M)\neq (1)$      314Ч315
$G_{2}$ holonomy, holonomy subgroups      245
$G_{2}$ holonomy, metrics Ricci-flat      244
$G_{2}$ holonomy, parallel spinors      245
$G_{2}$ holonomy, research problems      303Ч305 416Ч418
$G_{2}$, definition      242
$K3$ surface      155Ч162
$K3$ surface, examples      156
$K3$ surface, marked      157
$K3$ surface, moduli space      157 161
$L^p(M)$      see Lebesgue space
$L^{P}_{k}(M)$      see Sobolev space
$\hat{A}$-genus      67 164 259
$\mathbb{H}$      see Quaternions
$\mathbb{O}$      see Octonions
Age grading      130Ч132 200
ALE manifold      173Ч174
ALE manifold, analysis on      178Ч182
ALE manifold, asymptotic coordinates      174
ALE manifold, Calabi conjecture for      186Ч188
ALE manifold, Eguchi Ч Hanson space      153Ч154 160
ALE manifold, examples      177Ч178 393Ч394
ALE manifold, Hodge theory      183Ч184
ALE manifold, holonomy Spin(7)      345Ч346
ALE manifold, hyperk$\ddot{a}$hler      148 153Ч155
ALE manifold, K$\ddot{a}$hler      174 201
ALE manifold, radius function      174 175
ALE manifold, Ricci-flat K$\ddot{a}$hler      175Ч178
ALE manifold, structure group Spin(7)      344 393Ч394
ALE manifold, weighted H$\ddot{o}$lder space      176 179
ALE manifold, weighted Sobolev space      178
Ambrose Ч Singer Holonomy Theorem      32 37
Associative 3-fold      70 264Ч265 417
Associative 3-fold, examples      326Ч327
Asymptotically Locally Euclidean      see ALE manifold
Atiyah Ч Singer index theorem      19 67 259
BergerТs Theorem      55
Betti number      2
Betti number, refined      62 245 260
Bianchi identities      36 43 45 59
Blow-up      91Ч92 293
Bochner theorem      64 124
Bootstrap method      116 303 364
Calabi Conjecture      98Ч100
Calabi conjecture, for ALE manifolds      186Ч188
Calabi conjecture, for QALE manifolds      225 229
Calabi Ч Yau manifold      56 70 82 98 121Ч147 304
Calabi Ч Yau manifold, constructions      138Ч142 146
Calabi Ч Yau manifold, definition      123
Calabi Ч Yau manifold, deformations      142Ч144
Calabi Ч Yau manifold, Hodge numbers      125
Calabi Ч Yau orbifold      135 146 395Ч396 401-
Calibrated geometry      68Ч70 264Ч269
Calibrated submanifold      68
Calibration      68
Canonical bundle      94
Cayley 4-fold      70 267Ч268 417
Cayley 4-fold, examples      371Ч373
Cayley numbers      see Octonions
Characteristic class      94
Characteristic class, $\hat{A}$-genus      67 164 259
Characteristic class, first Chern class      94 97 98 122
Characteristic class, first Pontryagin class      246Ч247 259 261
Cheeger Ч Gromoll Theorem      64
ChowТs theorem      90 95 126
Coassociative 4-fold      70 265Ч267 417
Coassociative 4-fold, examples      327Ч328
Cohomology, de Rham      2 182
Cohomology, Dolbeault      77
Cohomology, Hodge numbers      85
Cohomology, of sheaves      89 93
Cohomology, other cohomology theories      2
Cohomology, Poincar$\acute{e}$ duality      3
Cohomology, with compact support      182
Compact linear map      6 103 179 187 226
Complete intersection      139 402 413
Complex manifold      72Ч75
Complex manifold, biholomorphism      74
Complex manifold, holomorphic function      72
Complex manifold, holomorphic map      74
Complex manifold, rigid      92 132 139
Complex projective space      73
Complex structure      72Ч73
Complex structure, almost      72
Complex symplectic manifold      162Ч164
Complex symplectic manifold, irreducible      162
Complex symplectic manifold, marked      163
Complex symplectic manifold, moduli space      163
Connection      20Ч25
Connection, Levi Ч Civita      40 42Ч43
Connection, on principal bundle      23
Connection, on tangent bundle      33Ч38
Connection, on vector bundle      22
Connection, torsion-free      35Ч38
Continuity method      104
Crepant resolution      126Ч132
Crepant resolution, of $\mathbb{C}^{m}/G$      175 210
Curvature and holonomy groups      32Ч33
Curvature in principal bundles      24
Curvature in vector bundles      22Ч23
Curvature of K$\ddot{a}$hler metrics      81Ч82
Curvature, Ricci      44
Curvature, Riemann      43Ч44
Curvature, scalar      44
de Rham theorem      2
Deformation      92Ч93
Deformation, of $\mathbb{C}^{m}/G$      132 201 238
Deformation, of Calabi Ч Yau manifold      142Ч144
Deformation, smoothing      92 313 318 324
Deformation, universal      93
Deformation, versal      93
Dirac operator      65Ч68 259 260
Divisor      96Ч97
Divisor, exceptional      91 127
Divisor, prime      96
Dolbeault cohomology      77
Douady space      166 215
Double point      127
Double point, ordinary      127
Double point, rational      129
EbinТs Slice Theorem      252
Eguchi Ч Hanson space      153Ч154 160 177 212 311 313 370 374
Elliptic equation nonlinear      250
Elliptic operator      7Ч19
Elliptic operator, $L^{p}$ estimate      14
Elliptic operator, definition      9 11
Elliptic operator, existence of solutions      16Ч19
Elliptic operator, kernel finite-dimensional      17
Elliptic operator, nonlinear      10 100
Elliptic operator, regularity      13Ч16 297 303 364
Elliptic operator, Schauder estimate      14Ч15 180
Elliptic operator, symbol      9 11
Exterior form      see Form
Fano manifold      168
FLOP      128
FORM      1Ч4
Form, $G$-structure splitting      59Ч60
Form, Hermitian      78
Form, holomorphic volume      122
Form, hyperk$\ddot{a}$hler 2-form      151
Form, K$\ddot{a}$hler      79 122
Form, of type $(p,q)$      77
Form, on K$\ddot{a}$hler manifolds      82Ч84
Form,complex symplectic      150
Frobenius theorem      48
GreenТs representation      14 181
H$\ddot{o}$lder space      5Ч6
H$\ddot{o}$lder space, weighted      176 179 221
H$\ddot{o}$lderТs inequality      4
Harmonic coordinates      298
Hilbert scheme      166 215
Hodge numbers      85
Hodge numbers, of hyperk$\ddot{a}$hler manifolds      164
Hodge star      3 60
Hodge star, on K$\ddot{a}$hler manifolds      83
Hodge theory      4 61Ч63
Hodge theory, on ALE manifolds      183Ч184
Hodge theory, on K$\ddot{a}$hler manifolds      84Ч85
Holomorphic vector bundle      77
Holonomy algebra      28 30 45
Holonomy group, and cohomology      59Ч64
Holonomy group, and curvature      32Ч33
Holonomy group, classification      55Ч59
Holonomy group, constant tensors      34Ч35
Holonomy group, definition      26 29 45
Holonomy group, exceptional      see $G_2$ holonomy Spin(7) etc.
Holonomy group, for principal bundles      29Ч32
Holonomy group, for vector bundles      25Ч29
Holonomy group, restricted      28 29 45
Holonomy group, Ricci-flat      58
Holonomy group, Riemannian      44Ч45
Hypercomplex algebraic geometry      171 215
Hypercomplex manifold      148 167 170
Hyperk$\ddot{a}$hler manifold      57 98 148Ч167 169
Hyperk$\ddot{a}$hler manifold, ALE      148 153Ч155
Hyperk$\ddot{a}$hler manifold, examples      165Ч167
Hyperk$\ddot{a}$hler manifold, Hodge numbers      164
Hyperk$\ddot{a}$hler manifold, moduli space      165
Hyperk$\ddot{a}$hler manifold, QALE      211 213Ч215 239
Hyperk$\ddot{a}$hler manifold, twistor space      151Ч152
Hyperk$\ddot{a}$hler quotient      154 169
Hyperk$\ddot{a}$hler structure      148 151
Hypersurface      96
Hypersurface, Calabi Ч Yau      139
Hypersurface, degree $d$      139
Hypersurface, in toric variety      142
Hypersurface, in weighted projective space      140 401
Implicit Mapping Theorem      7 253 263
Injectivity radius      5 221 292Ч295 298 359- 399
Instanton      169 269
Interior estimate      16
Intrinsic torsion      40
Inverse mapping theorem      7 118 228
K$\ddot{a}$hler chamber      158
K$\ddot{a}$hler class      80 85 175 210
K$\ddot{a}$hler cone      85 158 175 210
K$\ddot{a}$hler form      79 122
K$\ddot{a}$hler manifold      56
K$\ddot{a}$hler metric      79
K$\ddot{a}$hler potential      80
K$\ddot{a}$hler potential type      215 229
Kodaira embedding theorem      96 125
Kondrakov Theorem      7 16 103
Kummer construction      137 156Ч157 160Ч161
Kuranishi family      94 143
Laplacian      3 7 10 14 61
Laplacian, on ALE manifolds      180Ч182
Laplacian, on K$\ddot{a}$hler manifolds      83 105 198
Laplacian, on QALE manifolds      220Ч225
Lebesgue space      4Ч5
Lefschetz hyperplane theorem      97 140 404
Levi Ч Civita connection      40 42Ч43
Line bundle      94Ч96
Line bundle, ample      95 125
Line bundle, canonical      94 122 126
Line bundle, first Chern class      94 97 98 122
Line bundle, over $\mathbb{CP}^m$      94
Line bundle, positive      96
Line bundle, very ample      95
Maximum principle      16 222
McKay correspondence      129 131 154 309
Metric, Fubini Ч Study      53 80
Metric, Hermitian      78
Metric, hyperk$\ddot{a}$hler      151
Metric, K$\ddot{a}$hler      79
Metric, reducible      46Ч50
Metric, symmetric      50Ч55
Mirror Symmetry      142 145Ч146
Moduli space      63 169
Moduli space, of $G_2$-manifolds      251Ч254
Moduli space, of $K3$ surfaces      157 161
Moduli space, of complex symplectic manifolds      163
Moduli space, of hyperk$\ddot{a}$hler manifolds      165
Moduli space, of Spin(7)-manifolds      261Ч264
Monge Ч Amp$\grave{e}$re equation      100
Newlander Ч Nirenberg theorem      72
Nijenhuis tensor      72
Node      127
Octonions      57
Orbifold      132Ч136
Orbifold, Calabi Ч Yau      135 146 395Ч396 401^02
Orbifold, complex      133 166
Orbifold, crepant resolntion      136Ч139
Orbifold, group      133
Orbifold, K$\ddot{a}$hler      134
Orbifold, of torus      137 278Ч280 346Ч347
Orbifold, point      133
Orbifold, real      133
Parallel transport      26
Period domain      158 163
Period domain, hyperk$\ddot{a}$hler      161 165
Period map      143 157 163
Period map, hyperk$\ddot{a}$hler      161 165
Picard group      94
Poincar$\acute{e}$ duality      3
Principal bundle      20
Principal bundle, connection      23
QALE manifold, analysis on      219Ч225
QALE manifold, Calabi conjeclure for      225 229
QALE manifold, definition      208 236Ч238
QALE manifold, examples      212Ч215 239Ч241 276Ч278
QALE manifold, generalized      235Ч241
QALE manifold, holonomy $G_2$      277Ч278
QALE manifold, holonomy Sp($m$)      211 213Ч215 239
QALE manifold, holonomy Spin(7)      345Ч346
QALE manifold, holonomy SU($m$)      211Ч213 239
QALE manifold, K$\ddot{a}$hler      208Ч210 238
QALE manifold, K$\ddot{a}$hler potentials      215
1 2
blank
–еклама
blank
blank
HR
@Mail.ru
       © Ёлектронна€ библиотека попечительского совета мехмата ћ√”, 2004-2019
Ёлектронна€ библиотека мехмата ћ√” | Valid HTML 4.01! | Valid CSS! ќ проекте