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| Mimura M., Toda H. — Topology of Lie Groups, I and II |
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| Предметный указатель |
 theory 157
(J.H.C.) Whitehead theorem 86
(J.H.C.) Whitehead theorem, mod C 160
(tangent) vector field 40 78
Adem relation 102 103 406 408
Adjoint action 257 258
Adjoint group 279
Adjoint map 165
Adjoint representation 80 81
Blakers — Massey theorem (mod ) 161
Bockstein, exact sequence 99
Bockstein, homomorphism 99
Bockstein, mod p Bockstein homomorphism 101 146
Borel little (transgression) theorem 378
Borel transgression theorem 378
Bott map 200
Bott periodicity 207 210
Cartan formula 102 405 407
Cartan subalgebra 337
Center 6 72 74 268 296
Center of Schlaefli diagram 298
centralizer 6 258
Characteristic class 135 227 380
Chern character 196 197
Chern class 136 137 231
Chern, total Chern character 197
Chern, total Chern class 197 230
Classical group 24 72 118
Classical group, of infinite dimension 179
Classical group, projective 72
Classifying space 88 90 147 378 388
Classifying theorem 87 88
Cohomology, group (ring) 98
Cohomology, operation 102 403 418
Cohomology, stable operation 102 403
Comparison theorem 373
Complete (Riemannian manifold) 308
Complex cell 85
Complex cubical chain 93 94
Conjugate point 311
Connected, arcwise 14
Connected, locally arcwise 14
Connected, n-connected 67
Connected, simply 49
Covering, (universal) covering group 71
Covering, homotopy property 64 66
Covering, homotopy theorem 61
Covering, regular covering space 53
Covering, space 49 50
Covering, transformation group 52
Covering, universal covering space 53
Coxeter diagram 289
Cross section 59
Cross section, local 59
Cross section, mod p 219
CW-complex 85
Decomposable 356
Decomposable, indecomposable 356
Defect 320 337
Duality theorem 228
Dynkin diagram 289
Dynkin diagram, extended 294
Eilenberg — MacLane space (complex) 158 402
Euler characteristic 258 388 392
Euler class 117 146 389 392
Exceptional (Lie) group 293
Exceptional point 310
Exponential map 308
Fibration 64 105
Fibration, locally trivial 55
Fibration, principal 113
Fibration, relative 106
Fibre bundle 55 57
Fibre bundle, associated 60
Fibre bundle, associated principal 60
Fibre bundle, n-universal 86
Fibre bundle, relative 106
Finite type 101
Focal point 311
Freudenthal theorem (mod &) 161
Fundamental (cohomology) class 391 402
Fundamental group 49
Geodesic 308 320
Geodesic, mod N 310
Geodesic, segment 309
Geodesic, segment mod N 310
Gysin exact sequence 117
H-group 164
H-group, co- 164
H-space 69 168 174 372
H-space, co- 163
Haar integral 239
Harris decomposition 220
Height 356
Homogeneous space 8 9 147
Homology group 96
Homology group, with local coefficients 103
Homotopy, (weak) homotopy equivalence 48 86
Homotopy, class 48
Homotopy, exact sequence 63
Homotopy, extension property 86
Homotopy, group 62
Homotopy, semistable homotopy group 216
Homotopy, stable homotopy group 216
Hopf algebra 173 356 358
Hopf algebra, fibering 213
Hopf algebra, quasi 173 358 365
Hopf — Borel theorem 366
Hopf — Samelson theorem 371
Hurewicz homomorphism 155
Hurewicz mod Hurewicz theorem 156
Hurewicz Theorem 156
Hyperplane 270 272 339
INDEX 311
Infinitesimal diagram 270
Infinitesimal K-motion 316
Initial vector 39
Integer lattice 263
Invariant integral 239
Irreducible (root system) 289
Isometry (isometric transformation) 246
Isotropy group (stabilizer) 10
Jacobi identity 76
Jacobi vector field 310
K-cycle 348 354
k-group 192 207 210
K-transversal 316
| KF-group 192 194 200
KO-group 192 207 210
KSp-group 192 210 211
Kudo transgression theorem 408
Kunneth formula 97 99
Lefschetz fixed point theorem 258 398
Lefschetz number 398
Leray theorem 399
Leray — Hirsh theorem 127
Lie algebra 76 79 279
Lie group 39 80 279 280
Linear Lie group 43
Linear, general linear group 14
Linear, special linear group 15
Manifold, (regular) submanifold 38
Manifold, differentiable 37
Manifold, topological 36
Maximal torus 128
Maximal torus, standard 28 128
Monogenic 255 359
Morse inequality 314
Morse series 314
Morse theory 312 350
Nondegenerated 310
Normal matrix 24 26
normalizer 6
Obstruction theory 231
One-parameter subgroup 40 268 320
Orthogonal group 18 19
Orthogonal group, complex 21
Orthogonal group, of infinite dimension 179
Orthogonal group, special 18
Orthonormal basis 18
periodicity 200 204 207 210
Periodicity of K-groups 204 207 210
Periodicity of KO-groups 207 210
Periodicityof Ksp-smups 210 211
Poincare duality theorem 392
Poincare polynomial 101
Poincare series 101 315
Polar decomposition 34 36
Pontrjagin class 143 231
Pontrjagin class, total 231
primitive 174 356
Primitive, primitively generated Hopf algebra 368
Primitive, principal bundle 59
Projective space 123 125
Puppe exact sequence 167
Rank 223 261 343
Rank, subgroup of maximal rank 151 297
Reflection 270
Regular element 267
Regular point 310 337
Regular representation 399
Regular sequence 383
Riemannian invariant metric 247 323
Riemannian manifold 247
Riemannian metric 246
Root 263 265 352
Root, dominant 293
Root, inverse 274
Root, negative 285
Root, positive 285
Root, simple 285
Schlaefli diagram 289
Serre exact sequence 111
Serre spectral sequence 109
SIMPLE 280
Simple factor 280
Simple system 367
Simple, semisimple 280
Singular element 267
Spectral sequence 110 112 113 374
Spectral sequence, positive 374
Spinor group 74 82 177
Spinor group, semi 74
Stabilizer (isotropy group) 316 319 330
Steenrod, algebra 406 408
Steenrod, reduced power operation 102 406
Steenrod, squaring operation 102 141 405
Stiefel diagram 272 339
Stiefel — Whitney class 139 140 230
Stiefel — Whitney class, total 230
Suspension, image 377
Suspensive 377
Symmetric pair 146 322
Symmetric space 146
Symmetric space of classical type 147
Symmetric space of infinite dimension 181 184
Symmetric space, irreducible 147
Symplectic group 21 22
Symplectic group, complex 23
Symplectic group, real 23
Symplectic Pontrjagin class 136 137
Tangent bundle 38
Tangent bundle, space 38
Thom class 116 390
Thom Isomorphism 116 390
Topological group 5 75
Topological manifold 36
Topological transformation group 8
Torus 255 257
Torus, maximal 257 258 336
Torus, standard maximal 265
Totally nonhomologous to zero 127
Transgressive 377
Transgressive, universally 380
Type (of Lie group) 223 341 347
Type (of Lie group), (geodesic) variation 309
Unitary group 19
Unitary group of infinite dimension 179
Unitary group, special 19
Universal coefficient theorem 97 98
Variational completeness 318 324 327 328
Vector bundle 190
Vector bundle, conjugate 191
Vector bundle, stable equivalence of 194
Wang exact sequence 169
Weight 269 283
Weight, fundamental 295
Weyl, cell 272 340
Weyl, chamber 270 271 339
Weyl, extended group 272
Weyl, fundamental cell 294
Weyl, fundamental chamber 285
Weyl, group 28 131 133 261 270 339 393
Wu formula 424
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