1-form 73
Adjoint representation 46
Algebraic bracket 135
Algebraic derivation 134
Almost complex structure 142
Anholonomic 17
Associated bundle 158
Atlas 3
Base 12 61
Base space 143
Basis manifold 143
Betti number 88
Bianchi identity 144
Bundle 143
Caley — Hamilton equation 201
Canonical flip 67
Cech cohomology set 62
Center 55
centralizer 55
Characteristic class 194
Chart 3
Charts with boundary 85
Chern character 206
Chern classes 205
Chern — Weil form 194
Chern — Weil homomorphism 194
Christoffel forms 146
Classical complex Lie groups 39
Classifying spaces 163
Closed form 88
Cocurvature 140
Cocycle condition 62 143
Cocycle of transition functions 62 143
Cohomological integral 111
Cohomologous 62 154
Cohomology classes 62
Cohomology group 92
Cohomology of the Lie algebra 130
Compatible 61
complete 20
Complete connection 147
Conjugation 45
Connection 140 144
Connection form, Lie algebra valued 172
Connector 187
Contact of order 209
Cotangent bundle 73
Covariant derivative 187
Covariant exterior derivative 176 189
Curvature 140 188
Curvature form, Lie algebra valued 173
Curve of local diffeomorphisms 24
De Rham cohomology algebra 88
De Rham cohomology algebra with compact supports 99
Degree 119
densities 81
Density or volume of the Riemannian metric 83
Derivation 6
Derivations, graded 134
Diffeomorphic 4
Diffeomorphism 4
Differential 9
Differential form 74
Differential group of order 211
Distinguished chart 29 33
distribution 28 29
Effective action 55
Ehresmann connection 148
Equivalent 3 61
Euler — Poincare characteristic 89
Evolution operator 35
Exact 80
Exponential mapping 43
Exterior derivative 77
f-dependent 141
F-related 21 141
Fiber 61
Fiber bundle 143
Fiber chart 143
Fibered composition of jets 211
Fibered manifold 12
First non-vanishing derivative 24
Flow line 19
Flow prolongation 71
Foliation 31
Frame field 17 64
free 55
Frolicher — Nijenhuis bracket 136
Fundamental vector field 57 58
G-atlas 154
G-bundle 154
G-bundle structure 154
Gauge transformations 166
General linear group 37
Geometric objects 214
Germ of f at x 6
global 20
Graded derivations 134
Graded differential space 91
Grassmann manifold 156
Haar measure 122
Hairy ball theorem 119
Half space 85
Holonomic 17
Holonomic frame field 17
Holonomous 73
Holonomy group 149 179
Holonomy Lie algebra 149
Homogeneous space 56
Homomorphism of G-bundles 161
Homomorphism over  of principal bundles 157
Homotopy operator 90
Horizontal bundle 144
Horizontal differential forms 176
Horizontal foliation 145
Horizontal lift 144
Horizontal projection 144
Horizontal space 140
Horizontal vectors 144
Ideal 54
Idealizer 55
Immersed submanifold 13
Immersion at 12
INDEX 208
Induced connection 183 184
Induced representation 165
Infinitesimal automorphism 31
Initial submanifold 14
Inner automorphism 45
insertion operator 76
Integrable 28 31
Integral curve 19
Integral manifold 30
Integral of the density 81
Invariant of the Lie algebra 193
Invertible 213
Involution 67
Involutive 28 33
Irreducible *-principle connection 180
| Jet at 209
k-form 74
k-th order frame bundle 214
Leaf 31
Left action 55
Left invariant 40
Left invariant differential form 121 127
Left logarithmic derivative 47
Lie algebra 18
Lie bracket 18
Lie derivation 135
Lie derivative 22 70 75
Lie group 36
Lie subgroup 52
Linear connection 186 187
Linear frame bundle of 162
Local diffeomorphism 4
Local vector field 17
Long exact cohomology sequence with compact supports 111
Manifold pair 97 111
Manifold with boundary 85
Maurer — Cartan equation 146
Maurer — Cartan form 47
Maximal 30
Natural bilinear concomitants 142
Natural bundles 214
Natural lift 71
Natural transformation 71
Natural vector bundle 68
Nijenhuis tensor 142
Nijenhuis — Richardson bracket 135
normalizer 55
One parameter subgroup 42
Orbit 55
Orientable 84
Orientable double cover 114
Orientations 84
Oriented manifold 84
Orthogonal group 37
Orthonormal frame bundle 163
Orthonormal frame field 163
Pfaffian class 205
Plaque 29 33
Poincare polynomial 89
Pontryagin character 202
Pontryagin classes 197
Pontryagin numbers 199
Principal (fiber) bundle 154
Principal bundle atlas 154
Principal connection 172
Principal fiber bundle homomorphism 157
Principal right action 155
PRODUCT 10
Projection 61 143
Proper homotopy 100
Proper smooth mappings 99
Pullback 145
Pullback vector bundle 65
Pure 3
Quaternionic unitary group 40
Quaternionically linear 40
Quaternionically unitary 40
Reduction of the structure group 157
Relative De Rham cohomology 97
Relative De Rham cohomology with compact supports 111
Representation 45
Restricted holonomy group 149 179
Riemannian metric 162
Right action 55
Right invariant 41
Right logarithmic derivative 46
Right trivialized derivative 123
Section 61
Semidirect product 59
Short exact sequence 92
Signature 118
Singular foliation 31
Smooth distribution 30
Smooth functor 64
Smooth partitions of unity 5
Source mapping 209
Source of a jet 209
spans 29
Special linear group 37
Special orthogonal group 37
Special unitary 39
Sphere 4
Stable 31
Stably equivalent 199
Standard fiber 61 143
Stereographic atlas 4
Stiefel manifold 156
Structure 3
Submanifold 9
Submanifold charts 9
Submersion 12
Support 5 61
Support of a vector field 20
Symplectic group 38
Tangent bundle 8
Tangent space of M at x 7
Tangent vector 6
Target mapping 209
Target of a jet 209
Tensor field 71 73
Time dependent vector field 35
Todd class 207
Topological manifold 3
Total Chern class 205
Total Pontryagin class 197
Total space 12 61 143
Trace classes of a complex vector bundle 206
Trace coefficients 199
Transformation formula for multiple integrals 81
Transition functions 61 143
Transitive action 55
Transversal 15
Truncated composition 210
Typical fiber 61
Unimodular Lie group 122
Unitary 39
Universal vector bundle 169
Vector bundle 61
Vector bundle atlas 61
Vector bundle chart 61
Vector bundle functor 68
Vector bundle homomorphism 64
Vector bundle isomorphism 64
Vector field 17
Vector product 39
Vector subbundle 28 64
Vector valued differential forms 134
Vertical bundle 67 144 170
Vertical lift 67
Vertical projection 67 144
Vertical space 140
Volume 83
Volume bundle 81
Zero section 61
Zero set 5
|
|
|
О проекте