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Audin M. — Torus Actions on Symplectic Manifolds
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: en

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

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Meridian      21
Merindol, Jean-Yves      2
Milnor join      178
Milnor, John      109 177 178 182 212
Mineur, Henri      90
Moduli space      148 212
Moebius strip      20 25
Molino, Pierre      2
Momentum mapping      73 93
Momentum mapping, canonical      75
monodromy      150
Morse function      112
Morse function on the complex projective space      107 110
Morse lemma      108
Morse theory      3 7 105
Morse — Bott function      108
Morse, Marston      3 108
Moser path method      48
Moser, Jurgen      48
Negative normal bundle      109
Nijenhuis tensor      65
Noether theorem      79
Noether, Emmy      79
Numerable bundle      178
Numerable covering      178
Numerical image      5
Orbifold      25 85 101
Orbifold symplectic      85
Orbit      10
Orbit mapping      10
Orbit method      3
Orbit space      13
Orbit type      10 16
Orbit, exceptional      18 20
Orbit, principal      17 18 20
Orbit, singular      18 20
Orthogonal group      11 32
Oscillator, harmonic      103
Pair of pants      164
Pantalon      164
Path method of Moser      48
Pendulum, simple      88 90 93
Pendulum, spherical      103
Period lattice      91
Periodic Hamiltonian      79
Permutahedron      6 118 143
Pfaffian      42
Plumbing      300 308
Poincare lemma      49
Poisson bracket      59 60 73
Poisson manifold      60
Poisson mapping      73
Poisson structure      60 86
Poisson structure on the moduli space      155
Poisson structure on the space of quadratic forms      67
Poisson submanifold      62
Prato, Elisa      2 85
Primitive polyhedron      122 233 244
Principal action      17 38
Principal bundle      21 170
Principal orbit      17 18 20
Problem of Toeplitz and Hausdorff      5 105 113
Procesi, Claudio      193
Projective completion      18
Projective line      23
Projective plane      18 38
Projective space      37 51
Projective space, weighted      102 268
Racaniere, Sebastien      2
Raymond, Franck      21
Real structure      68
Reconstruction      110
Reduced symplectic form      83—85 186 191 258
Reduction in stages      100
Reduction, symplectic      83
Reeb, Georges      279
Reyman, Alexei      2
Riemannian metric      15
Riemannian volume      58
Rinkel, Jean-Marc      2
Rubenthaler, Hubert      2
Sabbah, Claude      3
Satake      85
Schur — Horn theorem      6 105 117
Schur, Issaie      6
Seifert fibration      25 32
Seifert invariants      26 27 29 30 39
Seifert manifold      7 8 18 24 25 30 80 85 86 273 308
Seifert, Horst      21
Semi-free action      13 38
Semi-simple group      41 75
Sevennec, Bruno      2 54
Simple group      12
simple pendulum      88 90 93
Simple polyhedron      122
Simplicial cone      233
Singular orbit      18 20
Singularity      25
Skeleton of a fan      229
Skew-Hermitian matrix      39
Skew-symmetric matrix      40
Slice theorem      14 15 20
Slupinski, Marcus      2
Smooth fan      233
SO(2,1)-orbit      40
SO(3)-orbit      40
SO(4)-orbit      41
SO(N)      33
Souriau, Jean-Marie      60 72
Space of affine lines      64
Space, homogeneous      35
Special orthogonal group      33
Special unitary group      41
Sphere      18 47
Spherical pendulum      103
Spielberg, Holger      2
Stabilizer      10
Stationary phase      209
Sternberg, Shlomo      193 201
Stiefel manifold      183 184
Stokes formula      28 46
Structure, almost complex      53
Structure, complex      53
Structure, real      68
SU(2)-manifold      80 99 131 139 144 146 271
Support of a fan      229
Support of a module      201
Symplectic $S^{1}$-actions on surfaces      97
Symplectic basis      44 65
Symplectic blow down      288
Symplectic blow up      103 223
Symplectic cut      103 139
Symplectic foliation      62 87
Symplectic form      45
Symplectic form on $C^{n}$      62
Symplectic form on $P^{1}(C)$      64
Symplectic form on $P^{n}(C)$      52
Symplectic form on a cotangent      46
Symplectic form on a Grassmannian      100
Symplectic form on a U(n)-orbit      52
Symplectic form on coadjoint orbits      62
Symplectic form on the complex projective space      84
Symplectic form on the moduli space      155
Symplectic form on the set of affine lines      64
Symplectic form on the sphere      47 64
Symplectic form on the torus      47
Symplectic form, reduced      83—85 186 191 258
Symplectic gradient      58
Symplectic group      45 62 64
Symplectic leaf      62 155 159
Symplectic Lie algebra      45
Symplectic manifold      43 46
Symplectic measure      209
Symplectic normal bundle      49 64
Symplectic orbifold      85 101
Symplectic reduction      83 84 100 102
Symplectic teardrop      101
Symplectic vector space      43
Symplectic volume      47 58 209
Tangent cone      227
Tangent map to the momentum mapping      78
Teardrop      101
Theorem of Arnold and Liouville      71 88 89
Theorem of Cartan      35
Theorem of convexity of Atiyah and Guillemin — Sternberg      7 105 113
Theorem of Darboux      48 102 118 119 194
Theorem of Delzant      2 105 122 123 225
Theorem of Duistermaat and Heckman      1 7 177 192 199 208 258 273 297
Theorem of fibration of Ehresmann      91 123
Theorem of Frankel      105 109
Theorem of Kushnirenko      105
Theorem of Noether      79
Theorem of Schur and Horn      105 117
Thom class      213 217
Thom Isomorphism      213 215
Thom, Rene      3 213
Toeplitz — Hausdorff problem      5 105 113
Toeplitz, Otto      5 113
Tolman, Suzan      2 85
Toric manifold      225 234
Toric variety      225
Torus      11 18 33 47 74
Torus of Liouville      89
Torus, big      239
Torus, compact      32
Torus, complex      32
Torus, maximal      61
Transitive action      13
Trinion      164 166
Trivial action      12
Trivial connection      148
Tubular neighborhood      14
TYPE      10 16
U(n)-orbit      38 43 50 56
Unitary basis      44
Unitary group      11 12 32 39
Universal bundle      178
V-manifold      25 85
Vanhaecke, Pol      2
Vector field, fundamental      10
Vector field, Hamiltonian      58
Vector field, locally Hamiltonian      58
Vector space, symplectic      43
Vergne, Michele      7 177
Verlinde formula      170
Very ample line bundle      252
Wall crossing formula      201 274
Weight      119
Weighted projective space      102 268
Weinstein, Alan      48 60 85
Weitsman, Jonathan      2 164 169
Wurzbacher, Tilmann      2
Zeugma      107
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