Audin M. — Torus Actions on Symplectic Manifolds :: Электронная библиотека попечительского совета мехмата МГУ

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Audin M. — Torus Actions on Symplectic Manifolds

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Название: Torus Actions on Symplectic Manifolds

Автор: Audin M.

Аннотация:

This is an extended second edition of The Topology of Torus Actions on Symplectic Manifolds published in this series in 1991. The material and references have been updated. Symplectic manifolds and torus actions are investigated, with numerous examples of torus actions, for instance on some moduli spaces. Although the book is still centered on convexity theorems, it contains more results, proofs and examples.

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: Second revised edition

Год издания: 2004

Количество страниц: 325

Добавлена в каталог: 02.02.2010

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Предметный указатель

$T^{n}$       33
$\mathcal{H}_{\lambda}$       12 38
(H)      10 16
Action coordinates      89 90 93
Action, adjoint      33
Action, effective      12
Action, free      13 38
Action, Hamiltonian      3 72
Action, principal      17 38
Action, semi-free      13 38
Action, transitive      13
Action, trivial      12
Action-angle coordinates      89 96 103 104 164
Adjoint action      33 61
Adjoint orbit      40 41
Adjunction formula      206
Affine structure      90
Alekseev, Anton      2
Algebra of Lie      32
Almost complex structure      53 58
Almost complex structure on a surface      53
Almost complex structure, calibrated      53 65
Almost periodic Hamiltonian      106 107
Angle coordinates      89 95
Antipodal map      18
Arnold — Liouville theorem      71 88 89
Arnold, Vladimir      8 90 97 129
Atiyah and Guillemin — Sternberg convexity theorem      7 105 113
Atiyah, Sir Michael      4 105 126 155 156 177
Basis, symplectic      44
Basis, unitary      44
Berline, Nicole      7 177
Beschler, Edwin      3
Bezout, Etienne      27
Big torus      239
Blow down      288
Blow up      103 193 215 223 239 286 289 299 307
Borel construction      7 177 183 189 212
Borel, Armand      7
Bott, Raoul      110 155 156 177
Bouyakoub, Abdelkader      2 272
Bracket of Lie      32 33 59
Bracket of Poisson      59 60
Brion, Michel      2 193 212
Bundle, cotangent      46
Bundle, principal      21
Calibrated almost complex structure      53 58 107
Calibrated almost complex structure, invariant      56
Calibrated complex structure      65
Cannas da Silva, Ana      2
Canonical form      46
Canonical momentum mapping      75
Cartan formula      49 59 71 93
Cartan theorem      35
Cartan, Elie      35 148
CHARACTER      119
Chiang, River      2
Chow ring      260
Class of Euler      21—24 31 32 39 134 185 187 188 192 193 206 207 214 216 218 220 222 226 235 257 258 260 266 273 274 279 290 291 298 303 310
Class of Thom      213 217
Classification Theorem      18 29 131 135 244 271 272 289
Closedness      46 52 60 67
Closing a fan      233
Coadjoint action      61 75
Coadjoint orbit      61 62
Cohomology of a blow up      215
Cohomology of a Grassmannian      222
Cohomology of BT      185
Cohomology of de Rham      175 184
Cohomology of moduli spaces      212
Cohomology of the projective space      185 214 222
Coisotropic submanifold      49
Coisotropic subspace      83
Compact torus      32
Complete fan      229 235 244 249 252 256 259 260 269
Complete flag      51 117 142 144
Completely integrable system      87
Completely integrable torus action      87 120
Complex manifold      53 56 58
Complex projective space      51 107 110
Complex structure      53 66
Complex structure on a U(n)-orbit      57
Complex torus      11 32
Connectedness of the levels of the momentum mapping      112
Connection      148
Connection, flat      149
Connection, integrable      149
Connection, trivial      148
Continued fraction      300 302
Contractibility of the infinite sphere      182 221
Contractibility of the infinite Stiefel manifold      183
Contractibility of the Milnor join      182 221
Contractibility of the space of calibrated almost complex structures      54 55
Convex hull      5 6 114 118 129
Convex polyhedron      7 75 105 114 117 118 126 129 141 143 166 167 225 226 229 244 252 255 267
Convexity theorem      1 6 113 117 126 136 166 226
Cotangent bundle      46
Curvature form      174 176 186 258
Curvature mapping      148 156
Curvature of a connection      148
Curvature of a Riemannian metric      50
Cylindrical coordinates      64
Danilov, Vladimir      7 226
Darboux theorem      48 102 118 119 194
Darboux, Gaston      102
De Rham cohomology      175 184 217
Delzant uniqueness theorem      105
Delzant, Thomas      1 2 7 271
Demazure, Michel      225
Desolneux-Moulis, Nicole      2
Direct limit topology      179
Divisor      194
Dolbeault operator      66
Dold, Albrecht      177
Donaldson, Simon      169
Dual of a Lie algebra      60 75
Duistermaat, Hans      177
Duval, Julien      2
Effective action      12
Ehlers, Fritz      261
Ehresmann fibration theorem      91 123
Equivariant cohomology      7
Equivariant Darboux Theorem      50
equivariant Euler class      214
Equivariant map      9
Equivariant mapping      10
Equivariant proof      50
Equivariant tubular neighborhood      14
Erlangen program      3
Euler class      21—24 31 32 39 134 185 187 188 192 193 206 207 214 216 218 220 222 226 235 257 258 260 266 273 274 279 290 291 298 303 310
Euler class, equivariant      214
Exact form      46
Exactness      46
Exceptional divisor      194 196 215 223 287
Exceptional orbit      18 20 24 26
Exponential mapping      15 34
Facet      229
Fan      225 226 228 229 292
Fan, complete      229 235 244 249 252 256 259 260 269
Fan, smooth      233
Fibration of Seifert      32
First integral      88
First quadrant      75
Fixed points      16
Fixed points of a group action      3
Fixed points of a Hamiltonian action      77 105 114 116
Flag manifold      51 56
Flag, complete      51 117 142 144
Flat connection      149
Flat module      205

Fock, Vladimir      2 161
Form of Liouville      45 46 64
Form, canonical      46
Form, symplectic      45
Formula of Cartan      49 59 71 93
Formula of Stokes      28 46
Formula of Verlinde      170
Formula, wall crossing      201 274
Fougeront, Jacques      2
Frankel theorem      105 109
Frankel, Theodor      4 272
Free action      13 38
Fubini — Study metric      66
Fundamental vector field      10 33 73
Fundamental vector field for the U(n)-action      67
G-action      9
G-manifold      9
G-vector bundle      10
Gatien, Daniel      2
Gaucher, Philippe      2
Gauge group      149
Geodesic flow on the sphere      68 100
Gerardy, Sophie      2
Ginzburg, Viktor A.      2 6 113 177
Ginzburg, Viktor G.      2
Givental, Alexander      8
Godinho, Leonor      2
Goldman function      162 163 165
Goldman system      165
Goldman, William      2 162 163
Gradient      58
Gradient sphere      286 287 289 290 292
Gradient, symplectic      58
Grassmannian      42 100 101 141 170 183 222
Group of holonomy      150
Group of Lie      32
Group, linear      32
Group, orthogonal      32
Group, semi-simple      41 75
Group, simple      12
Group, special orthogonal      33
Group, special unitary      41
Group, symplectic      45 62 64
Group, unitary      12 32 39
Guillemin, Victor      1 2 193 201
Gysin exact sequence      214
Gysin homomorphism      206 215 217
Haar measure      15
Hamiltonian      58
Hamiltonian action      3 72
Hamiltonian circle action on $S^{2}$       77
Hamiltonian circle action on a surface      97
Hamiltonian mechanics      3
Hamiltonian R-action      74
Hamiltonian system      88 96
Hamiltonian torus action on $P^{n}(C)$       76
Hamiltonian torus action on $\mathcal{H}_{\lambda}$       76
Hamiltonian vector field      58
harmonic oscillator      103
Hausdorff, Felix      5 113
Heckman, Gert      177
Hermitian matrix      6 12 50
Hexagon      6
Hirzebruch surface      132 133 135 137 138 143—146 224 237 262 263 266 281 282 288 289 292
Hodge star operator      41
Holonomy group      150
Holonomy of a loop      150
Homogeneous coordinates      106
Homogeneous space      11 35
Homotopy quotient      184
Hopf fibration      23 24 192 218 219 278 279
Horn, Alfred      6
Identity of Jacobi      32 33 52 59 60 67
Identity of Leibniz      59 60
Iglesias, Patrick      2 131 282
Image, numerical      5
Index of a critical submanifold      109
Inoue surface      310
Integrable complex structure      58 66
Integrable connection      149
Integrable system      71 87 96 104
Integrable system of Goldman      164 165
Integration in the fibers      216
Invariant calibrated almost complex structure      56
Invariant metric      15
Irrational flow on the torus      11 13 37
Isotropic      82
Isotropic submanifold      49
Isotropic subspace      83
Jacobi identity      32 33 52 59 60 67
Jacobian      152
Jeffrey, Lisa      2 161 164 169 212
Jurkiewicz, Jerzy      261
Kaehler form      58
Kaehler form on $C^{n}$       66
Kaehler form on $P^{n}(C)$       66
Kaehler manifold      58
Kaehler metric      58
Karasev, Mikhail      177
Karshon, Yael      2 8 272
Khovanski, Askold      129
Kirillov, Alexander      3 60
Kirwan, Frances      7 112 136 212 226 247
Klein bottle      19
Klein, Felix      3
Kostant, Bertram      3 60
Krein — Milman theorem      250
Kushnirenko theorem      105
Kushnirenko, Anatoly      4 129
Lack      3
Laeng, Laurent      2
Lagrange, Joseph Louis      3
Lagrangian submanifold      49
Lagrangian subspace      65
Lagrangian torus      89 95
Leaf, symplectic      62
Lebesgue measure      96 209
Leibniz identity      59 60
Leibniz rule      73
Lens space      27 39 182 223 303 304 310
Lerman, Eugene      85 102
Level set      79 81
Li, Jie      2
Libermann, Paulette      2
Lichnerowicz, Andre      60
Lie algebra      9 32
Lie algebra of the orthogonal group      40
Lie algebra of the symplectic group      67
Lie algebra of the unitary group      39
Lie bracket      32 33 59
Lie group      9 32
Lie subgroup      10
Linear group      11 32
Liouville form      45 46 64 93 97
Liouville torus      89
Liouville, Joseph      45 90
Local exactness      46
Localization formula      207
Localization theorem      204 212
Locally Hamiltonian vector field      58 72
Loop group      159 161
Lopez de Medrano, Santiago      2
Manifold, complex      53
Manifold, symplectic      46
Marie, Charles-Michel      50
Maximal torus      61
McDuff, Dusa      2 8 103 272 276 289
Measure of Haar      15
Measure of Lebesgue      96 209
Measure, symplectic      209

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