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| Greub W., Halperin S., Vanstone R. — Connections, curvature, and cohomology. Volume 1 |
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| Предметный указатель |
Product of tensor fields 118
Product of vector bundles 46 84 378
Product, exterior 120
Product, manifold 29ff. 97 110 121 139 148 256
Product, orientation 127 289
Product, tensor 55
Projection map 29
Projective module 7 78 86 106
Projective space, complex 42 415
Projective space, quaternionic 42
Projective space, real 23 85 125 138 415
Proper homotopy 191
Proper map 190 273
Pseudo-Riemannian vector bundle 66 85
Pull-back 48 72 82 84 85 315
Pull-back, of cross-section 325
Quaternions 2 42 275
Quotient bundle 84
Quotient manifold 101 122
Radial neighbourhood 112
Radial vertical vector field 292
Rank of vector bundle 44 55
Real projective plane embedded in  138
Real projective space 23 85 125 187 376 415
Refinement of open cover 14
Regular point 136
Regular value 136 244
Relative cohomology 349
Relative Euler class 349
Restriction of vector bundle 46
Restriction of vector field 109
retract 104 183
Retract, deformation 184
Retrenchment 300
Riemann coordinate representation 68
Riemann metric 66
Riemann vector bundle 66 70
Riemann — Hurwitz relation 386
Rotation number 277
Rouche's theorem 275
Sard's theorem 136
Scalar product 2 52 see "Metric"
Scalar product Poincare 194
Sec  60
Second countable space 14
Second tangent bundle 134
Short exact sequence 84
Shrinking of open cover 17
Sig(M) 206
Signature of manifold of dim 4k 206
Signature of scalar product 2
Simple open cover 218
Simplex, affine 236 388
Simplex, ordered, of nerve 217
Simplex, smooth 231
Simplex, standard 231
Simplicial complex 217 236
Simplicial homology 234 236 389
Simply connected manifold 235
Skew symmetric p-linear functions 5 51 79 61
Skew tensor product of algebras 4
Skew transformations 72
Smooth atlas 22
Smooth family 153
Smooth fibre bundle 38
Smooth function 30
Smooth homology 231
Smooth manifold 22 28ff. 35ff.
Smooth map 12 24ff. 88 99ff.
Smooth path 35
Smooth structure 22 29
Solid angle 171
Space, base 38
Space, bundle 38
Space, cohomology 9
Space, cotangent 97
Space, differential 9
Space, Euclidean 2
Space, Hermitian 2
Space, paracompact 14
Space, second countable 14
Space, tangent 87
Space, topological 14
Space, total 38
Sphere bundle, associated 105 293
Sphere bundle, cohomology of 316ff. 344
Sphere bundle, cross-sections of 338
Sphere bundle, Euler class of 320 328
Sphere bundle, induced orientation of 293
Sphere bundle, vector bundles and 291
Spheres 22 24 26 34 93 104 128 166 175 184 262 270 408
Spheres, cohomology of 185ff.
Spheres, Euler — Poincare characteristic of 186
Spheres, Hopf fibering of 42
Spheres, Lefschetz class for 395
Spheres, maps of 262
Spheres, orientation of 124
Spheres, Poincare polynomial of 186
Spheres, product of 215 250
Spheres, vector fields on 375
Sprays 135 418
Sprays, flow of 419
Standard simplex 231
Star-finite open cover 217
Star-shaped domain 170 183
Stiefel manifolds 348
| Stokes' theorem 167ff. 170
Stokes' theorem for chains 233
Stokes' theorem for fibre integrals 311
Strong bundle maps 45 50
Strong bundle maps, dual of 52
Strong bundle maps, module of 50 61
Structure, complex 73
Structure, homogeneous 414
Structure, manifold 22 39
Structure, smooth 22
Structure, Symplectic 173
Sub-manifolds, open 23
Subbundle 44 68
Subbundle, horizontal 282
Subbundle, vertical 280
Submanifold 103
Submersion 99 313
Substitution operator 6 141
Support see "Carrier"
Suspension 266
Symbol of differential operator 133 134
Symmetric algebra 5 58
Symmetric multilinear functions 5 51 61
Symplectic bundle 85
Symplectic manifold 172
t 167
Tangent bundle 94ff. 385
Tangent bundle of fibre bundle 280ff.
Tangent bundle of product manifold 97
Tangent bundle, cross-section of 106
Tangent bundle, second 134
Tangent space 87
Tangent vector 87
Tensor field 118
Tensor product 4 7 55
Tensor product, external 84 86
Th,  355
Thom class of fibre bundle 355
Thom class of fibre bundle of vector bundle 359 370
Thom class of fibre bundle, Euler class and 364
Thom class of fibre bundle, Lefschetz class and 397
Thom Isomorphism 355 380
Topological manifold 15ff. 41
Topological space 14
topology 14
Torsion 175
Torsion groups of manifold 232
Torsion parallel 235
Torus 23 41 215 228 230 248
Total space 38
Transversality theorem of Thom 416
Transverse regular map 416
Trivial bundle 46 76
Trivializing map 44
Trivializing neighbourhood 44
Tubular neighbourhood 138
Typical fibre 38
Unit tensor 8 81 118
Universal coefficient theorem 232
Van Est's theorem 313
Vector bundles 44ff. 291ff. see
Vector bundles, Cartesian product of 46 84 378
Vector bundles, complex 73 86
Vector bundles, construction principle of 47
Vector bundles, double cover induced by 71
Vector bundles, dual of 52
Vector bundles, endomorphism of 85
Vector bundles, isometry of 67 68
Vector bundles, orientation in 292
Vector bundles, pull-back of 48 84
Vector bundles, restriction of 46
Vector bundles, symplectic 85
Vector bundles, tensor product of 55 84 86
Vector bundles, trivial 46 76
Vector bundles, Whitney sum of 54
Vector fields 106ff. 131
Vector fields on  378
Vector fields on real projective space 376
Vector fields on sphere 375
Vector fields parallel 174
Vector fields,  -related 109
Vector fields, constant 108
Vector fields, flow generated by 113
Vector fields, Lie product of 108
Vector fields, local one-parameter group generated by 114
Vector fields, M-product of 111
Vector fields, orbit of 112
Vector fields, restriction of 109
Vector, cotangent 96
Vector, differential forms with, values 149 163
Vector, tangent 87
Vertical cohomology 313
Vertical component 282
Vertical subalgebra 283
Vertical subbundle 281
Vertical subspace 280
Vertical vector 280 281
Wang sequence 229
Whitney sum 54 68 76 84
Whitney — Graustein theorem 277
Whitney's embedding theorem 137
Winding number 276
Zero index 332
Zero measure 136
Zero section 59
[x, y] 107
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