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

Ossa      139
Ozsvath      453
Packing problem      249
Palais      97 409
Palais — Smale condition      409—411
Palais — Smale condition and asymptotics of H      409
Parallel transport      208 210
Periodic orbit existence      265
Periodic orbit structure near      265
Periodic point infinitely many      274
Peschke      424
Peters      136 446
Poenaru      262
Poincare duality      132 133
Poincare section map      266 269
Poincare section map is symplectomorphism      267
Poincare — Birkhoff theorem      1 36 265 269 280 339
Poincare — Birkhoff theorem for monotone twist maps      277
Poisson bracket      23 86
Poisson bracket in contact geometry      111
Poisson commuting functions      24
Poisson geometry      2
Poisson structure      11 22
Poisson structure on dual Lie algebra      169
Pollack      185
Polterovich      100 181 226 232 243 246 249 252 300 325 366 383 384 391 392 401
Principal bundle      207
Quadratic growth      403
Quadratic growth and Palais — Smale condition      409
Quadratic growth generating function      358
Quantization      5
Quaternions and SU(2)      166
Rabinowitz      2 30 402
Ramanan      251
Reduction      see “Symplectic reduction”
Reeb vector field      106 111
Riemann surface Arnold’s conjecture for      339
Riemann surface as symplectic manifold      89
Riemann surface as the quotient $\mathbb{H}/\Gamma$       206
Riemann surface Darboux’s theorem for      98
Riemann surface Euler class of complex line bundle over      79
Riemann surface first Chern number on      74
Riemann surface Hofer — Zehnder capacity      400
Riemann surface integrability for      126
Riemann surface loops and 1-forms on      255
Riemann surface symplectic isotopy on      98
Riemann surface trivializations of vector bundles over      72
Rigidity      2 33 34 280 324
Rigidity of symplectomorphisms      377—380
Robbin      50 54 280 283 288 290 293 304 347
Ruan      146 333 373 436
Rudyak      304 344
Ruled surface      135 159 197 204 248 249 439 442
Ruled surface symplectomorphism group      333
Salamon      25 29 35 50 54 146 280 283 288 290 293 304 347 351 369 373 452
Schechter      128
schur      182
Seiberg — Witten invariants      4 439
Seidel      197 207
Sevennec      65
Shiohama      427
Siebert      141 146 373
Siegel      265 275
Siegel domain      116
Siegel upper half space      48
Sign conventions      23 84
Sign conventions for moment map      152
Sikorav      3 309 358 364 371
Singer      312
Sjamaar      169 179
Smale      409
Sniatycki      201 211
Stability problem for flows      268
Stable manifold      183
Stasheff      69 203
Stern      446
Sternberg      5 151 159 160 162 180 197 207 210 215 226 242 250 312
Sternberg — Weinstein universal construction      160 197 207 250
Structural group of fibration      69 198
Struwe      399
Submanifold clean intersection of      174
Submanifold coisotropic      99; see “Coisotropic”
Submanifold isotropic      99
Submanifold Lagrangian      99
Submanifold Legendrian      106 309
Submanifold symplectic      99
Submanifold symplectic existence of      450
Submanifold totally real      123
Surface classification      134
Surface Dolgachev      135
Surface elliptic      135
Surface general type      135 139
Surface K3      134 446
Surface rational      147
Surface ruled      135 147 159 204 248 249 439 442
Surgery (cont.) Contact      252
Surgery (cont.) Symplectic      252
Surgery along Lagrangian tori      252
Symp(M)      311—315
Symp(M) $\pi_1$ of      322
Symp(M)algebraic structure      328
Symp(M)algebraic structure when M noncompact      329
Symp(M)as $\infty$ -dimensional Lie group      312
Symp(M)for noncompact manifolds      314 320
Symp(M)is -enclosed in Diff(M)      377
Symp(M)locally path connected      311
Symp(M)topology of      333
Symp(M)universal cover of      315
Symplectic 4-manifold blowing up and down      248
Symplectic 4-manifold geography      446
Symplectic 4-manifold have arbitrary $\pi_1$       254
Symplectic 4-manifold minimal      249
Symplectic 4-manifold nonKaehler as twisted connected sum      445
Symplectic 4-manifold rational      249
Symplectic 4-manifold ruled      249
Symplectic 4-manifold uniqueness for ball      430
Symplectic 4-manifold uniqueness for star-shaped regions      43
Symplectic action      see “Action”
Symplectic affine group      55
Symplectic ball      see “Ball”
Symplectic basis      42 57;
Symplectic blowing up and down      see “Blowing up and down”
Symplectic camel problem      32 426
Symplectic capacity      see “Capacity”
Symplectic complement      38
Symplectic connection      209
Symplectic connection Hamiltonian holonomy      215—226
Symplectic connection holonomy      210
Symplectic embedding manifold into $\mathbb{C}P^n$       251
Symplectic embedding of balls      3
Symplectic embedding spaces      246
Symplectic energy      380; see “Energy”
Symplectic fibration and blowing up      250
Symplectic filling      420
Symplectic form      20; see “Symplectic form”
Symplectic form cohomologous      422
Symplectic form cohomology class of      83
Symplectic form cohomology class of and blowing up      239 241
Symplectic form cohomology class of on fibrations      202
Symplectic form deformation equivalent      145 247 422
Symplectic form diffeomorphic      422
Symplectic form geometry compared with Riemannian      1 82 83 88 95 96 426
Symplectic form gradient      17
Symplectic form group action and fibrations      156
Symplectic form group action examples      166
Symplectic form homotopic      422
Symplectic form isomorphic      422
Symplectic form isotopic      97 422
Symplectic form on vector bundle      69
Symplectic form pseudo-isotopic      247 422

Symplectic form strongly isotopic      97 422
Symplectic form symplectomorphic      422
Symplectic form weakly deformation equivalent      422
Symplectic homeomorphism      379
Symplectic homology of polydisc      429
Symplectic invariant      366
Symplectic invariant for closed manifolds      434—439
Symplectic invariant for manifolds with boundary      429—433
Symplectic invariant for noncompact manifolds      427—429
Symplectic invariant local versus global      1
Symplectic invariant noncompact manifold volume of end      428
Symplectic invariant of cohomological type      427
Symplectic invariant of open ellipsoid      428
Symplectic invariant of open polydisc      429
Symplectic isotopy      88 97
Symplectic isotopy extension theorem      97
Symplectic linear balls      376
Symplectic linear group      43—48
Symplectic linear group affine      55
Symplectic manifold      81—104
Symplectic manifold $\mathbb{C}P^n$       see “Complex projective space”
Symplectic manifold $\mathbb{R}^{2n}$       see “Euclidean space”
Symplectic manifold $\mathbb{T}^{2n}$       see “Torus”
Symplectic manifold and almost complex structures      117—129
Symplectic manifold and contact structures      112
Symplectic manifold and Kaehler manifolds      140 418
Symplectic manifold asymptotically flat are diffeomorphic to $\mathbb{R}^{2n}$       432
Symplectic manifold boundary information in      430
Symplectic manifold convex at infinity      426
Symplectic manifold cotangent bundle      see “Cotangent bundle”
Symplectic manifold deformation equivalent but nonisotopic      436
Symplectic manifold examples      89—93
Symplectic manifold Kodaira — Thurston manifold      89 156 251
Symplectic manifold Kodaira — Thurston manifold as fibre symplectic manifold connected sum      253
Symplectic manifold monotone      138 145 156
Symplectic manifold nonKaehler      90 117 251
Symplectic manifold not deformation equivalent      436
Symplectic manifold of Lefschetz type      154 324
Symplectic manifold of nonpositive curvature      426
Symplectic manifold uniqueness for ball in $\mathbb{R}^4$       430
Symplectic manifold uniqueness for star-shaped regions in $\mathbb{R}^4$       431
Symplectic manifold with boundary of contact type embedding balls in      432
Symplectic manifold with disconnected boundary of contact type      432
Symplectic matrix      19
Symplectic matrix eigenvalues of      45
Symplectic matrix neighbourhood theorem      81 100
Symplectic matrix neighbourhood theorem for hypersurfaces      104
Symplectic matrix positive definite      45 64
Symplectic quotient      152
Symplectic reduction and Arnold’s conjecture      369
Symplectic reduction and blowing up      242 251
Symplectic reduction linear      40 43
Symplectic reduction moduli spaces      179
Symplectic reduction of coisotropic submanifold      173
Symplectic spectrum      60
Symplectic structure      11 81
Symplectic structure characterized by capacity      377
Symplectic structure existence on open manifolds      257—262
Symplectic structure exotic on $\mathbb{R}^{2n}$       100
Symplectic structure explicit exotic form on $\mathbb{R}^{4}$       424
Symplectic structure induced by immersion      420
Symplectic structure nature of      33 34 37
Symplectic structure nonexistence on spheres      83
Symplectic structure on -bundles      159
Symplectic structure on $\mathbb{R}^{2n}$       82
Symplectic structure on 4-torus      444
Symplectic structure on coadjoint orbit      168
Symplectic structure on cotangent bundles      90
Symplectic structure on reduced space      173
Symplectic structure uniqueness      422
Symplectic submanifold      3 99
Symplectic submanifold existence of      450—453
Symplectic subspace      38 42
Symplectic topology      1
Symplectic vector bundle      68—71
Symplectic vector space      38—42
Symplectic versus volume-preserving maps      377
Symplectic width      371 374
Symplectic width linear      56
Symplectization      see “Contact manifold”
Symplectomorphism      11 18 83
Symplectomorphism action spectrum      299
Symplectomorphism affine      55
Symplectomorphism as discrete flow      286
Symplectomorphism characterized by capacity      377
Symplectomorphism condition to be Hamiltonian      294
Symplectomorphism exact      294
Symplectomorphism exact of torus      327
Symplectomorphism Hamiltonian      see “Hamiltonian symplectomorphism”
Symplectomorphism linear      38
Symplectomorphism near identity as graph of 1-form      102 302 311
Symplectomorphism of cotangent bundle      92
Szabo      446 453
Taubes      4 34 83 140 418 439
Telescope construction      257
Theret      309 358 369
Thorn conjecture      453
Thurston      89 90 197 199 200 253 329 419
Tian      35 141 146 172 369 373
Tischler      251
Tolman      155 180
Topological Lefschetz fibration      455
Toric manifold      see “Manifold”
Torus and squeezing      373
Torus Arnold’s conjecture      34 339
Torus as base of -bundle      205
Torus as fibre      201
Torus calculation of flux      325
Torus condition for exactness      314
Torus connected sum along      253
Torus exact symplectomorphism of      327
Torus fixed points for symplectomorphism near identity      342
Torus generating function on      341
Torus group action has isotropic orbits      163
Torus group action on toric manifold      178
Torus Hamiltonian flow on      34
Torus invariant under flow      268
Torus Lagrangian      252
Torus moment map for      169
Torus proof of Arnold’s conjecture      345
Torus rigidity in cotangent bundle of      364
Torus symplectic structures on      444
Torus symplectomorphism with 3 fixed points      342
Totally geodesic submanifold      27
Totally real submanifold      123
Totally real subspace      68
Traynor      33 181 249 373 426
Trivialization local of fibration      197
Trivialization of vector bundle      71—73
Trivialization symplectic      71
Trivialization unitary      71
TU      6 96 109 133 155 245 320
Twist map      see “Area-preserving”
Twisted framing      see “Connected sum”
Unitary group      see “Linear group”
Unstable manifold      183 349
Ustilovsky      392
van de Ven      120 136 446
Variational family for Lagrangian submanifold      306
Variational family transversal      307 308
Variational family universal with $\infty$ -dimensional fibres      309
Variational method finite dimensional      4
Variational Principle      402
Variational principle of least action      13 16
Variational principle of least time      12
Variational problem discrete time      277 286—288
Vector bundle complex      69
Vector bundle symplectic      68
Vector bundle trivialization      71
Vector field Liouville      30 113

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