McDuff D., Salamon D. — Introduction to Symplectic Topology :: Электронная библиотека попечительского совета мехмата МГУ

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McDuff D., Salamon D. — Introduction to Symplectic Topology

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Название: Introduction to Symplectic Topology

Авторы: McDuff D., Salamon D.

Аннотация:

Symplectic structures underlie the equations of classical mechanics and their properties are reflected in the behavior of a wide range of physical systems. Over the last few years powerful new methods in analysis and topology have led to the development of the modern global theory of symplectic topology, including several striking and important results. At its publication in 1995, Introduction to Symplectic Topology was the first comprehensive introduction to the subject and it has since become an established text in this fast-developing branch of mathematics. This second edition has been significantly revised and expanded, with new references and additional examples and theorems. It includes a section on new developments and an expanded discussion of Taubes and Donaldson's recent results.

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Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: 2nd edition

Год издания: 1998

Количество страниц: 486

Добавлена в каталог: 01.07.2006

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Предметный указатель

Hamiltonian symplectomorphism in kernel of flux      318
Hamiltonian symplectomorphism near identity      313
Hamiltonian symplectomorphism, group of      313
Hamiltonian system      11 14
Hamiltonian system and principle of least action      16
Hamiltonian system integrable      24 25
Hamiltonian time-dependent      88
Hamiltonian vector field      17 85 313
Hano      89
Hard-soft dichotomy      81 262 325
harmonic oscillator      26
Harmonic oscillator nonlinear analogue      29
Harris      136 154 237 238 445 450
Hattori      433
Heckman      159 191 192
Herman      29 30 328 329 399
Hermitian structure      70
hilbert      128
Hirzebruch signature theorem      137 446
Hirzebruch surfaces      136
Hofer      2—4 30 32 35 146 299 358 369 371 373 377 380 382 384 391 394—396 398—403 416 429 430
Hofer metric      280 299 371 380—383
Hofer metric variants      383
Hofer metric bi-invariance      381
Hofer metric calculation in terms of generating functions      391
Hofer metric coarse      391
Hofer metric diameter of $\textrm{Ham}(S^2)$       366
Hofer metric for Hamiltonian function      381
Hofer metric geodesic      392
Hofer metric geometric meaning      226 300 301
Hofer metric given by symplectic action      393
Hofer metric nondegeneracy      382
Hofer metric, local flatness of      391
Hofer — Zehnder capacity      384 394—397
Hofer — Zehnder capacity as area      400
Hofer — Zehnder capacity calculation for ball      397
Hofer — Zehnder capacity proof of axioms      401
Hofer — Zehnder capacity proof of conformality      396
Hofer — Zehnder capacity proof of monotonicity      396
Holonomy      208
Holonomy Hamiltonian      215 226
Holonomy of characteristic foliation      213
Holonomy of symplectic connection      210
Homogeneous space $GL(2n,\mathbb{R})/GL(n,\mathbb{C})$ complex structures      47 62
Homogeneous space $GL(2n,\mathbb{R})/Sp(2n)$ symplectic forms      42 47
Homogeneous space $GL^+(2n, \mathbb{R})/SO(2n)$ metrics      65
Homogeneous space O(2n)/U(n)      47
Homogeneous space SO(2n)/U(n)      62
Homogeneous space Sp(2n)/U(n)      45
Homogeneous space Sp(2n)/U(n) compatible complex structures      65
Homogeneous space Sp(2n)/U(n) has complex structure      48
Homogeneous space U(n)/O(n) Lagrangian subspaces      51
Hopf fibration      109 153
Hopf map      239
Hopf surface      201
Horizontal distribution      207 210
Hormander      307
Horn      182
Husemoller      69 119 120
Hyperplane field as contact structure      105
Hypersurface existence of periodic orbit      2
Hypersurface of contact type      30 113 426
Hypersurface of restricted contact type      114
Hypersurface, characteristic foliation of      29 87 99
Hypersurface, neighbourhood theorem for      104 245
Immersion exact Lagrangian      307 423
Immersion Legendrian      310
Immersion symplectic structure induced by      420
Index pair for isolated invariant set      347
Index pair regular      348
Inner product      63
Inner product Hermitian      63
Integrability theorem for almost complex structures      124 126
Integrability theorem Frobenius      105 124
Integrability theorem two-dimensional case      126
Integrable almost complex structure      123
Integrable Hamiltonian system      24
Integral of motion      22
Intersection of Lagrangian submanifolds      304
Invariant circle      268 269
Invariant set isolated      347
Invariant torus      24 268
Involution      100
Involution, functions in      24
Isotopy      97
Isotopy extension theorem      97
Isotopy of symplectic forms      97
Isotopy rel Y      97
Isotopy symplectic      97
Isotopy, fixed extrema of      392
Isotropic submanifold      99 104
Isotropic subspace      38 42
J-holomorphic curves      3 4 28 65 141—148 205 247 249 370 422 430 435 439
J-holomorphic curves bubbling      144
J-holomorphic curves positivity of intersections      146 148
J-holomorphic curves spheres      147
J-holomorphic map      244
Jacobi identity      23
Jeffrey      179 191
john      128
Kaehler manifold      130—140 253
Kaehler manifold and symplectic manifolds      140
Kaehler manifold as connected sum      254
Kaehler manifold Barlow surface      436
Kaehler manifold Calabi — Yau manifolds      139
Kaehler manifold Dolgachev surfaces      445
Kaehler manifold elliptic surface      237
Kaehler manifold hard Lefschetz theorem      140
Kaehler manifold K3 surface      134 136 446
Kaehler manifold minimal surface      134
Kaehler manifold of nonpositive curvature      426
Kaehler manifold positive      138
Kaehler manifold, surface of general type      139
Kaehler manifold, symplectomorphism group      333
Kaehler — Einstein metrics      172
KAM theory      25 268
Karshon      154 179 433
Kasper      202 436
Kepler problem      15 25
Kirwan      179 180
Kobayashi      72 124 207
Kodaira      89 90 134 248
Kodaira dimension      134
Kontsevich      141
Kostant      183
Kronheimer      72 124 139 179 207 453
Lafontaine      100
Lagrange multiplier      306
Lagrangian exact embedding      358
Lagrangian exact immersion      423
Lagrangian exact immersion and moment map      172
Lagrangian, frame      51
Lagrangian, functional      13 93
Lagrangian, immersions      359
Lagrangian, intersections      100 357—364
Lagrangian, neighbourhood theorem      101
Lagrangian, subbundle      70 80
Lagrangian, submanifold      11 25 99 101 113
Lagrangian, submanifold and symplectic reduction      174
Lagrangian, submanifold disjoined by isotopy      423
Lagrangian, submanifold exact      295 423
Lagrangian, submanifold exact embedding of      304
Lagrangian, submanifold generating function for      303—305 358—362
Lagrangian, submanifold intersections of      304
Lagrangian, submanifold invariant under flow      284
Lagrangian, submanifold none in $\mathbb{R}^{2n}$ are exact      423
Lagrangian, subspace      37 38 43 50—52 67
Lalonde      3 47 100 147 232 248 300 325 373 382 384 394
Lashof      201 211
Laudenbach      3 309 358

Lefschetz      154
Lefschetz fibration      215
Lefschetz fibration topological      455
Lefschetz fibration transformation      12 14 27 93 280
Lefschetz fixed point theorem      35 343
Lefschetz hyperplane theorem      135 139 452
Lefschetz pencil      140 238 456
Legendre condition      14 284 288
Legendrian immersion      310
Legendrian submanifold      106 113
Length of path in $\textrm{Ham}^c(M)$       381
Lerman      5 179 180 197 207 210 215 226 242
Level set connected      184
Level set with circle action      152
Levi — Civita connection and exterior derivative      121
Li      141 146 373 447
Libermann      104 162
Lie      151
Lie algebra coboundary      163
Lie algebra cocycle      163
Lie algebra cohomology      163
Lie algebra of contact vector fields      110 111
Lie algebra of derivations      85
Lie algebra of functions      86
Lie algebra of Hamiltonian vector fields      87
Lie algebra of Hamiltonian vector fields Hofer norm on      381
Lie algebra of symplectic vector fields      83
Lie algebra of vector fields      85
Lie algebra of vertical vector fields      220
Lie bracket sign of      23 84
Lie group action on T*G      167
Lie group coadjoint orbit as symplectic manifold      168
Lie group convexity of moment map      183
Lie group Hamiltonian action of semi-simple      169
Lie group Symp(M) as      312
Linear group $GL(n, \mathbb{C})$ and Sp(2n)      44
Linear group O(n) and $Sp(2n;\mathbb{R})$       44
Linear group SU(2) double covers SO(3)      166
Linear group symplectic      see “Symplectic linear group”
Linear group U(n) and Sp(2n)      44
Linear group U(n) compact in Sp(2n)      45
Linear map is symplectic iff preserves symplectic width      57
Linear symplectic ball      55
Linear symplectic cylinder      55
Linking argument to find critical points      411—416
Liouville vector field      30 113
Liouville’s theorem      20
Liu      35 140 141 146 369 447
Ljusternik — Schnirelmann theory      35 343 353—356
Localization theorem      159 191 192 194 195
Lupton      155 335
Luttinger      252
Lyapunov      355
Manifold $\infty$ -dimensional      25
Manifold 4-dimensional      132
Manifold almost complex structure on 6-manifolds      119
Manifold almost symplectic      86
Manifold closed      83
Manifold contact      see “Contact manifold”
Manifold open      257
Manifold stable      183 348
Manifold symplectic      see “Symplectic manifold”
Manifold toric      178 181 242 433
Manifold unstable      183 348
Marle      104 162
Marsden      5 151 265
Marsden — Weinstein quotient      175—179
Martin      191
Maslov cycle      49 52 53
Maslov index      48—50 52—54 290
Maslov index and Conley — Zehnder index      293
Maslov index as relative Morse index      370
Mather      277
Matrix determinant over $\mathbb{R}$ and $\mathbb{C}$       47
Matrix Schur — Horn theorem on eigenvalues      182
McCarthy      252
McDuff      3 29 33 47 90 147 155 181 204 232 237 243 246—251 300 325 369 373 382 384 392 394 419 426 430—432 435 452
Mechanics      5 151
Meckert      252
Meinrenken      180
Metaplectic representation      290
Meyer      265 275
Milinkovic      309
Milnor      50 69 135 185 203 342 343 453
Minimal reduction uniqueness of      249
Minimum of action      285
Moduli of J-holomorphic curves      141
Moduli spaces as reduced manifolds      179
Moment map      161—172
Moment map and equivariant cohomology      194
Moment map convexity      179—191
Moment map examples      165—170
Moment map image of      181
Moment map sign convention      152
Monotone embedding      240
Monotone symplectic manifold      156
Monotone twist condition      270 281
Monotonicity axiom for capacities      57 373
Monotonicity axiom for relative capacities      375
Montgomery      179
Morse index      349
Morse index relative      369
Morse inequalities      349—351
Morse inequalities and Floer theory      351
Morse theory      1 6
Morse theory for discrete symplectic action      351—353
Morse theory infinite dimensional      340
Morse theory on noncompact manifold      347
Morse-Bott function      183—185
Moser      25 95 265 275
Moser stability theorem      2 81 96
Moser stability theorem cohomological condition needed      435
Moser stability theorem for 2-manifolds      98
Moser stability theorem for volume forms      98
Moser’s argument      93 104 423
Mrowka      254 445 447 453
Muller      425
Mumford      179
Narasimham      251
Nash — Moser implicit function theorem      268
Nijenhuis tensor      123
Nomizu      72 124 207
Nondegenerate form      38
Nondegenerate form homotopic to almost complex structure      118 257
Nondegenerate form if closed is symplectic      81
Nonexistence of invariant      284
Nonsqueezing and tori      373
Nonsqueezing property      55
Nonsqueezing theorem      3 11 31 37 280
Nonsqueezing theorem affine      55—61
Nonsqueezing theorem and capacities      371—377
Nonsqueezing theorem for arbitrary manifolds      3 372
Nonsqueezing theorem for relative capacities      375
Nonsqueezing theorem proof      397
Nontriviality axiom for capacities      373
Norm invariant on Lie group      380
Normally hyperbolic critical manifold      183
Obstruction cocycle      163
Obstruction first Chern class      79
Obstruction for action to be Hamiltonian      162
Obstruction to existence of symplectic structure      262
Oh      309 357
Ohta      447
Ono      35 141 146 154 369 373 437 447
Oprea      155 304 335 344
Orbit connecting      369
Orbit periodic      1 265
Orbit periodic existence      396
Orbit T-periodic      394
Orbit variational formulation for      277 288

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