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| Greub W., Halperin S., Vanstone R. — Connections, curvature, and cohomology. Volume 1 |
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| Предметный указатель |
Exact triangle 10 178
Exponential map 13 26 28 136 395
Exponential map, generated by affine spray 421
Exponential of linear transformation 13
Exterior algebra 5 57
Exterior derivative 145
Exterior derivative, partial 148 312
Exterior product 120
External tensor product 84 86
Face of simplex of nerve 217
Face of smooth simplex 231
Family of cross-sections 153
Family of differential forms 154
Fibering of spheres 42 140 345 348
Fibre bundles 38 104
Fibre degree 383
Fibre integral 300
Fibre integration 289ff. 310
Fibre preserving map 39
Fibre projection 209
Fibre, typical 38
Fibre-compact carrier 295 298
Field of n-frames 170
Finite affine simplicial complex 236 389
Five-lemma 8
Fixed points 408
Fixed points, index of 407
Fixed points, isolated 414
Flow of spray 419
Flow, generated by vector field 113
Free involution 187
Free module 7
Frobenius' Theorem 134
Fubini's theorem 162 307
Function germs 32ff.
Functions 30
Functions, complex 274
Fundamental class 238 278
Fundamental cycle 237
Fundamental theorem of algebra 247
Germs of forms 188
Germs of functions 32ff.
Germs of maps 33
Global degree 240ff. 264
Global degree, dashed 386
Graded algebra 3 11
Graded differential space 10
Graded module 8
Gradient 115
Gram — Schmidt process 68
Grassmann manifolds 42 86
Green's formula 172
Gysin sequence 320ff. 382
H(M),  176
Half-space 139
Harmonic forms 231
Hermitian metric 2 27 74
hessian 138 379 416
Hodge theorem 231
Homogeneous linear map 8
Homogeneous structure 414
Homogeneous tensor 8
Homology, simplicial 234
Homology, smooth 231
Homomorphisms of algebras 2
Homomorphisms of differential spaces 9
Homomorphisms of graded differential algebras and spaces 11
Homomorphisms of graded modules 8
Homomorphisms of Lie algebras 4
Homomorphisms of vector bundles 45 see
Homotopy 33ff. 41 86
Homotopy, axiom 178 232
Homotopy, continuous 41
Homotopy, Contracting 183
Homotopy, lifting theorem 314
Homotopy, operator 9 178
Homotopy, orientation and 130
Homotopy, proper 191
Hopf fibering of spheres 42 140 345 348
Hopf index formula 377
Hopf invariant 229
Hopf theorem 266ff.
Horizontal subbundle 282ff.
i(x) 141
i-basis for topology 14
i-homotopy 277
Identification map for charts 22
Immersion 99
Inclusion map opposite point 97
INDEX 330 369 377
Index of fixed point 407
Index, (mod 2) 387
Index, degree and 332
Index, Euler class and 372
Index, sum 334 369 391 415
Induced orientation 66 373
Infinitely differentiable 12 see
Inner product 1 see "Scalar
Integral cohomology 233 310
Integral fibre 300 310
Integral line 234
Integral of smooth family of cross-sections 153
Integral of vector valued differential form 163
Integral over fibre 300 310
Integral over smooth p-simplex 233
Integration in manifolds 160ff. 174
Integration in vector spaces 159
Integration of n-forms 161 164
Integration over fibre 298ff. 310
Interchange map 29
Interior of manifold with boundary 139
Intersection theory 416
Invariant differential form 144 158
Inverse function theorem 12
Invisibility theorem 237
Invisible chain 236
Involution 71 122
Involution, canonical 135
Involution, free 187
Involutive distribution 134
Irreversible manifold 127 173 206 345
Isolated coincidence point 405
Isolated fixed point 414
Isolated point for map 259
Isolated singularity 329 385
Isolated zero 367
Isolated zero, manifold 384
Isometric vector bundles 67 68
Isometries of  348
Isomorphism 45 see
Jacobi identity 4
Jet bundles 132 134
Jet, of cross-section 134
Klein bottle 41 290
Kuenneth homomorphism 208 210 257
Kuenneth isomorphism 11 211 215
Kuenneth theorem 211 215
Laplace operator 172
Lebesgue dimension 17
Lebesgue measure zero 136
Lefschetz class 393 397
Lefschetz coincidence theorem 405
Lefschetz formula 11
Lefschetz isomorphism 393
Lefschetz number 401
Lefschetz theorem, weak 403
Legendre transformation 175
Leray 315
Lie algebra 4 107 152 173
Lie derivative 142
| Lie product 108
Limit, direct 238
Line integral 234
Linking number 276
Local coincidence number 405
Local decomposition of projection 38
Local diffeomorphism 99
Local flow of spray 419
Local one-parameter group 114
Local properties of smooth maps 99
Localization isomorphism 79
Localizing class 252
Locally Euclidean topological space 41
Locally finite open cover 14 31
Locally finite simplicial complex 217
Lorentz metric 414
Lusternik — Schnirelmann — Borsuk theorem 276
Manifolds, analytic 42
Manifolds, boundary of 139 231 350 415
Manifolds, cohomology algebra of 176
Manifolds, compact 41 203 218 228
Manifolds, connected sum of 140
Manifolds, contractible 86 183
Manifolds, double of 140
Manifolds, embedded 102
Manifolds, Grassmann 42 86
Manifolds, irreversible 127 206
Manifolds, metric 41
Manifolds, nonorientable 71 125 201
Manifolds, orientable 124 129 139 205 277
Manifolds, parallelizable 174
Manifolds, product of 29 110
Manifolds, quotient 101 122
Manifolds, retract of 104
Manifolds, simply connected 235
Manifolds, smooth 22 29 41
Manifolds, Stiefel 348
Manifolds, submanifolds of 103
Manifolds, symplectic 172
Manifolds, topological 15
Map, "product" 29
Map, orientation preserving/reversing 127
Map, power 28
Map, proper 190 273
Map, trivializing 44
Mapping, degree 240ff. 264
Mapping, transformations 45 47
Massey triple product 228
Mayer — Vietoris axiom 178 232
Mayer — Vietoris sequence 180 193 229 254
Metric see also "Inner product" "Scalar
Metric Hermitian 2 27 74
Metric Lorentz 414
Metric Riemannian 66
Metric, manifold with 41
Mixed tensor field 119
Mod 2, degree 274
Mod 2, index sum 387
Module 7ff.
Module of cross-sections 60 78
Module of derivations 106
Module of strong bundle maps 50
Module, bigraded 8
Module, finitely generated 76
Module, finitely generated projective 78
Module, free 7
Module, graded 8
Module, projective 78
Moebius ship 41
Morse 416
Morse functions 138
Morse lemma 138
Multilinear bundle map 47 82
Multilinear functions 5 51
Multiplication operator 6 209
n-forms, integration of 159ff.
Nerve of open cover 217
Nine-lemma 9
Noncompact carrier, forms with 164
Nondegenerate bilinear function 52
Nonorientable manifolds 71 125 201ff.
Normal bundle 138 380
Normed cross-section 66
o 104
One-form 115
One-parameter group 114 157 173
One-point compactification of complex plane 247
One-point compactification of Euclidean spaces 23 25
Open cover(ing) 14
Open cover(ing), nerve of 217
Open cover(ing), order of 17
Open submanifold 23 126
Open subset 14 23 89
Operator Laplace 172
Operator, differential 9
Operator, differential, of order p 133 134
Operator, gradient 115
Operator, homotopy 9 178
Operator, multiplication 6 209
Operator, substitution 6 141
Orbit of vector field 112 157
Ordered simplex 217 236
Orientable fibre bundle 285
Orientable manifold 72 124ff. 129 139 205 277
Orientable vector bundle 64
Orientation canonical of  126
Orientation class 201
Orientation of fibre bundl 285 310
Orientation of manifold 124
Orientation of sphere 124
Orientation of sphere bundle 293
Orientation of vector bundle 64 292
Orientation of vector space 1
Orientation, determinant function representing 64
Orientation, induced, of submanifold 126
Orientation, induced, of Whitney sum 66
Orientation, positive 64 70
Orientation, preserving/reversing map 127 287
Orientation, product 127 139
Oriented Riemann bundle 70
Orthonormal 2-frames 346
Orthonormal basis 68
Orthonormal vectors 348
Paracompact space, 14
Parallelism 174 175 235 278
Parallelizable manifold 174
Partial exterior derivative 148 312
Partition of unity 32
Path, smooth 35
Period of p-form 233
Permanent 5
Picard theorem 13 112
Poincare adjoint 400
Poincare duality 194ff. 201ff. 231 249
Poincare isomorphism 171 197
Poincare lemma 183
Poincare polynomial 178 186 215 345
Poincare scalar product 194
Poisson bracket 173
Positive basis 124
Positive n-form 124
Positive normed determinant function 70
Positive orientation 64 70
Positive self-adjoint linear map 26
Power map 28
Power, exterior 57
Power, symmetric 58
Product Lie 107
Product M, of vector fields 111
Product of spheres 215 250
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