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Mimura M., Toda H. — Topology of Lie Groups, I and II
Mimura M., Toda H. — Topology of Lie Groups, I and II



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Название: Topology of Lie Groups, I and II

Авторы: Mimura M., Toda H.

Аннотация:

Two treatments of the topology of Lie groups for senior students of mathematics, as a supplemental bridge between linear algebra and the more specialized disciplines that use it. The first book progresses from linear algebra to the periodicity of KO-groups; the second continues from the theory of compact Lie groups to exceptional groups. No bibliography.


Язык: en

Рубрика: Математика/Геометрия и топология/Алгебраическая и дифференциальная топология/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1991

Количество страниц: 451

Добавлена в каталог: 16.04.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$\mathscr C$ 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 $\mathscr C$)      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 $\mathscr C$ 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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