Milnor J.W., Stasheff J.D. — Characteristic Classes. (Am-76), Vol. 76 :: Электронная библиотека попечительского совета мехмата МГУ

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Milnor J.W., Stasheff J.D. — Characteristic Classes. (Am-76), Vol. 76

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Название: Characteristic Classes. (Am-76), Vol. 76

Авторы: Milnor J.W., Stasheff J.D.

Аннотация:

The theory of characteristic classes began in the year 1935 with almost simultaneous work by Hassler Whitney in the United States and Eduard Stiefel in Switzerland. Stiefel's thesis, written under the direction of Heinz Hopf, introduced and studied certain 'characteristic' homology classes determined by the tangent bundle of a smooth manifold.

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Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: 1st edition

Год издания: 1974

Количество страниц: 340

Добавлена в каталог: 14.04.2008

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Предметный указатель

      89 143 157ff
$H^{\Pi}$       39
, , L-genus      224ff 231 239ff
$\mathbf{R}$ , $\mathbf{R}^n$ , $\mathbf{R}^{\mathbf{A}}$ , $\mathbf{R}^{\infty}$ , $\mathbf{R}_0^n$       3 62 105 266f 270ff 278f
$\mathbf{R}_n$ -bundle      14 39 43
$\mathbf{R}_n$ -bundle, topological      251
$\mathcal{C}$ -isomorphism      207 233
Adams, J.F.      134 286
Alexander duality      280
Alexandroff line      23
Algebraic hypersurface      196
Almost complex structure      151
Associated bundle      139 195
Base space      13 27
Basis      10 23 95f 128
Bernoulli numbers       225 230 281ff
BF      252
Bianchi identity      297
Bilinear      21 31 48
Binomial coefficients      45f 94 184f
BO(n), BSO(n)      145 179 250ff see
Bockstein homomorphism      182 253
Bordant, bordism group      255
Borel, A.      134 189
Bott periodicity      244 255
Boundary      53 78 186 199 224
Boundary homomorphism      112 258 262
BU(n)      163
Bundle homotopy      65
Bundle map      26 37 42 61 65 98
Bundle of finite type      71
Canonical line bundle $\gamma^{1}$       16 43 71 93
Canonical n-plane bundle $\gamma^{n}$       59—71 141f
Canonical n-plane bundle $\gamma^{n}$ , complex      152 159—163 227f
Canonical n-plane bundle $\gamma^{n}$ , oriented $\tilde{\gamma}^{n}$       145
Cap product      113 135 233 276ff
Cartan formula      91
Cartesian product      3 27 34 54 64 92 100
Category      8 32 34
Cauchy — Riemann equations      150 153
Cayley numbers      48 134
Cell, cell structure      see "CW-complex"
Chain complex, mapping      111ff 182
Characteristic class      37 68f 250f 298
Characteristic map      73
Chern character      195f 296
Chern class $c_{i}$       38 155ff 174—177 182 189ff 220 243 299 306
Chern number      183ff 191ff
Chern product theorem      164
Chern — Weil theorem      311
Chern, S.-S.      v
Christoffel symbol      301
Classifying space      163 250ff 255 see "B()"
Closure finiteness      74
Cobordism      53f 197—203 211ff 223 253 256
Coboundary      258
Cohomology      89 257—280
Cohomology of       69 83—88 140 182 250
Cohomology of $G_n(\mathbb{C}^{\infty})$       102 189
Cohomology of       42 84
Cohomology of $P^n(\mathbb{C})$       159ff
Cohomology of $P^n(\mathbb{H})$       243
Cohomology of $\tilde{G}_n$       146 179ff
Cohomology of B Top      251
Cohomology of BF      252f
Cohomology of BPL      250 252f
Cohomology with compact support      275
Cohomology, generalized      254
Cohomotopy groups      208 233f 236 238f
Collar neighborhood      200
Combinatorial Pontrjagin classes      231—248
Complex analytic function      150
Complex manifold      150f 159
Complex n-plane (or vector) bundle      149
Complex structure J      149 173
Complexification $\otimes\ \mathbb{C}$       153 173ff
Conjugate bundle      167 170 173 176f
Connection $\nabla$       289—295 298ff 305ff 308 312
Connection $\nabla$ , Levi — Civita      300—302
Connection $\nabla$ , symmetric      301
Continuous functor      31
Coordinate neighborhood      4
Coordinate space      3
Coordinate system, local      4 19
Covariant derivative      289 301
Covering homotopy      70 206 252
Covering space      145 182 312 314
Cross product      92f 105 164 237
Cross-section      16ff 22ff 36 39 101f 139 142 152 289
Cup product      38 54 263ff
Curvature      31 293—300 306ff 310
Curvature, Gaussian      303 305
CW-complex      73—81 139—148 165 171 260ff 268ff
De Rham cohomology      289 298
Dependent cross-sections      18
Derivative      8ff 34 44
Derivative, covariant      289 301
Derivative, directional      9
Derivative, exterior      292
Determinant      295 299 309
df      8ff 34 44
Diagonal $\Delta$       93 100 121 123
Diagonal cohomology class      124 127ff
Diffeomorphism      7 9ff 14 42 48 115f 151 248 250
Differential form      253 290f 293ff 303f
Differential operator      9 153 290
Direct limit      63 108f 114 262 277ff
Division algebra      47ff
Dual bundle      33 35 152 168
Dual cohomology class      120 196 273
Dual vector space      9 31 169
Dyer — Lashof algebra      253
Embedding      10 70 81 115 120 135 148 196 211 215
Euclidean vector bundle or metric      21ff 28 35f 39 46 52 89 102 244 300 309ff
Euclidean vector space      21
Euler characteristic or Euler number      15 129f 148 170 184 186 313f
Euler class e      98ff 119f 123f 143—148 155 158 179f 243—247 309 311ff
Exponential map      116 124
Exterior derivative      292
Exterior form      295
Exterior power      31 70 148
Fiber       13f
Fiber bundle      14
Fibration      229 252 256
Flat connection      291 294 308 312
Foliation      253
Formal power series      221 224f
Frame      56 76 139
functor      8 32 34
Functor, continuous      31f
Fundamental class, cohomology      90—92 95 100 106ff 118f 123
Fundamental class, homology      50—52 126f 184 235 251 270 273
Gauss map      55 60 70
Gauss — Bonnet theorem      303ff 310f
Generalized cohomology theory      254
Generalized homology theory      255
Genus, K- or L-      223f
Geodesic coordinates      304
Girard's formula      195
Gram — Schmidt process      23 29 57 59
Grassmann manifold , $G_n(R^{n + k})$       55—65 68—88 102 245 250
Grassmann manifold , complex $G_n(\mathbb{C}^{n + k})$       102 152 159 163 171
Grassmann manifold , oriented $\tilde{G}_n$ , $\tilde{G}_n(\mathbb{R}^{n + k})$       145 179ff 214f 245f
Gysin sequence      143ff 157 160ff 180 243 245 247
Half space      75ff 199
Hermitian metric      156f 161 168
Hirzebruch, F.      38 219ff 224 231 241
Holomorphic      150—152
Hom      31 35 43 45 58 70 87 169f 248
Homology      257—263

Homology manifold      234—239
Homotopy class      69
Homotopy groups      206ff 212ff 245 250f 255 284
Homotopy type      223 226 229 245
Hurewicz homomorphism      207 246 252
Immersion      30f 49f 54 121
Implicit function theorem      209f
INDEX      224
Index theorem      226
Induced bundle      25f 149
Inner product      21
Invariant polynomial      295
Inverse function theorem      5 116
Inverse limit      108f 110f
Isometry      24
Isomorphic (vector bundles)      14 18 35f 38
J-homomorphism      284
Jacobian       8 30
jet      24
K-theory      254
Kronecker index      50 148 232 259
Kuenneth theorem      88 128 165 207 224 268f
Leibniz formula      289 292
Lens space      245
Linear group , $GL_n(\mathbb{R})$ , $GL_n(\mathbb{C})$       14 22 34 155
Local coefficients      140
Local coordinate system      4 13
Local operator      290
Local parameterization      4 199
Local triviality      13 149 152 249
Long line      23
Mapping cone      112
Mayer — Vietoris sequence      102 271f 278
Microbundle      250
MO(k), MSO(k)      215
Moebius band      17 94 120
Multiplicative characteristic class      227ff
Multiplicative sequence      219ff 224f 227ff
n-frame      56 76 139
n-plane      56 60
n-plane bundle      14 37
Naturality      37
Newton's formula      195
Normal bundle      15 23 29f 41 115ff 121 210 215 232 252
Obstruction      139ff 171 251
Oriented bundle      95ff 110 155 178f
Oriented cobordism      199ff 216
Oriented manifold      55 122 185f 200f 234 256 273ff
Oriented simplex      95
Oriented vector space      95
Orthogonal complement $\xi^{\perp}$       28f 35 43 70f 157 169
Orthogonal group      22 253
Pairing      21
Paracompact      23 28 62 65ff 71 74 240 291
Parallelizable      15 20 23 47f 148
Parameterization      4
Partition      80f 85 171 183—197 202 216 222
Partition of unity      23 210
Pfafian      309ff
Piecewise linear      235 237 249
Piecewise linear bundle      249
Piecewise linear manifold      239 247 249 252
Poincare complex      251f
Poincare duality      127ff 131 135 224 235 239 251 276ff
Poincare hypothesis      247
Pontrjagin classes       173—182 197 220 223ff 243f 308
Pontrjagin classes , combinatorial      231—248
Pontrjagin numbers      183 185f 193f 202 217 223f 226 247f 256
Pontrjagin, L.      v 52 186 202
Power series      40 221 224f 281 296
Product formulas      37f 100 164 175 190 227f
Projective module      36
Projective space, Cayley      134
Projective space, complex $P^n(\mathbb{C})$       133 152 159f 167 169f 177f 184f 189 192ff 202f 216 225 234
Projective space, quaternion $P^n(\mathbb{H})$       33 186 243 248
Projective space, real       11 15 42ff 49ff 55 70 80 94 120f 142 144
Quadratic function      21
Quaternions $\mathbb{H}$       20 48 243 248
Quotient bundle      35
Rank      4 85 181 216
Real vector bundle      13
refinement      183 195
Regular value      208ff 217 232 241
Representation ring      256
Restriction      25 270
Riemann surface      312
Riemannian connection      302
Riemannian manifold or metric      22 29f 35 115 121 253ff 300ff
Ring of smooth functions $C^{\infty}(M,\mathbb{R})$       10f
Sard's theorem      209 232
Schubert cell, Schubert variety      75 171
Schubert symbol $\sigma$       75—80
Second fundamental form      35 70
Serre, J.-P.      207 233
Sign conventions      258 304
Signature $\sigma$       224 232f 235ff 247
Signature theorem      224ff
Simplex $\Delta^n$       95f 234ff 257
Simplicial complex      234 237ff 249
Simplicial map      235ff
Singular homology and cohomology      37 258
Skeleton      260
Slant product      125f 131
Smooth function      4 7 34 70
Smooth manifold      3 4 9f 12 25 53 70 139
Smooth manifold with boundary      52 186 199ff 255 279f
Smooth path      5
Smooth vector bundle      14f 26 34 243
Smoothness structure      10f 248 250
Sphere bundle      38
Spinor group      253
Stable homotopy group      255
Steenrod reduced powers      228
Steenrod squares      90ff 130ff 182
Stiefel manifold      56 68f 139 145 171
Stiefel — Whitney class       37—50 54 83 119ff 130ff 140 171 181
Stiefel — Whitney class , axioms      37f 92
Stiefel — Whitney class , dual      49 87 136
Stiefel — Whitney class , existence      89—94
Stiefel — Whitney class , total      39f
Stiefel — Whitney class , uniqueness      86f
Stiefel — Whitney number      50ff 81 130 136 197 217 256
Stiefel, E.      v 38 47f
Stokes theorem      304
Structural group      14 22 34 253 294 312
Sub-bundle      27f 54 103
Sub-division      235 237
Submanifold      29f
Submersion      35
Symmetric function      84 87 186—191 222 230 299
Symplectic group      253
Tangent bundle $\tau$       14 21f 25 27 29f 41ff 70 87 121f 199f 243 251 249ff
Tangent bundle $\tau$ , complex      151 169 289
Tangent manifold DM      7ff 44
Tangent space       3 5 7ff 30 200 209f
Tangent vector      5 9f
Tensor product $\otimes$       31—36 87 149 173 289
Thom Isomorphism      90ff 97 99 105ff 119 207
Thom space      205—208 211ff 252
Thom, R.      53 91 193f 199ff 224 231
Todd genus      229
Topological manifold      57 251
Topology, direct limit      63f 74
Topology, direct limit, fine=large=Whitehead      63 74
Topology, weak      63
Total differential      9
Total space E( $\xi$ )      13 115 243
Trace      295 306
Transversality      205 208—215
Triangulation      139 143 240 247 251

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