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Michor P.W. — Gauge Theory for Fiber Bundles
Michor P.W. — Gauge Theory for Fiber Bundles



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Название: Gauge Theory for Fiber Bundles

Автор: Michor P.W.

Язык: en

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

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1988

Количество страниц: 105

Добавлена в каталог: 16.04.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$c^\infty$-topology      6
$C^\omega$-manifold structure of $C^\omega(M, N)$      19
$C^\omega$-manifold structure on $C^\infty(M, N)$      19
$\alpha$-respecting connection      100
$\mu$-respecting connection      92
$\omega$-respecting connection      98
Algebraic bracket      28
Algebraic derivation      27
Anti self dual      99
Approximation property (bornological)      15
Associated bundle      48
Associated vector bundles      52
Base space      36
Basis      36
Bianchi identity      37
Bundle      36
Bundle atlas      36
Bundle of gauges      54
Cartesian closedness      8 11 13
Characteristic class      94
Chern class      97
Christoffel forms      39
Classifying connection      87
Classifying space      53 87 89
Cocurvature      33
Cocycle condition      36
Cocycle of transition functions      36
Cohomologous      44
Complete connection      41
Connection      32 37 92
Connection form      95
Connection form (Lie algebra valued)      60
Connector      69
Continuous derivation over eva      14
Convenient vector space      7
Covariant derivative      63 70
Covariant derivative on vector bundles      70
Covariant exterior derivative      63 71
Curvature      32 33 37 70
Curvature form      96
Curvature form (Lie algebra valued)      60
De Rham cohomology of M with twisted coefficient domain $H^{n-1}(p)$      92
Derivations (graded)      27
Diffeomorphism group      22
Ehresmann connection      41
Equivariant mappings and associated bundles      50
Exponential law      20
f-dependent      33
F-related      33
Fiber bundle      36
Fiber bundle atlas      36
Fiber chart      36
Fiber volume      90
Fiberwise symplectic form      98
Flat connections      38
Frame bundle      81
Frolicher — Nijenhuis bracket      29
Fundamental vector field      5
G-atlas      44
G-bundle      44
G-bundle structure      44
Gauge group of a fiber bundle      83
Gauge transformations      54
General Bianchi identity      33
Generalization of the theorem of Ambrose and Singer      77
Global formula for the Frolicher — Nijenhuis bracket      30
Grassmann manifold      46
Hodge-*-operator      99
Holomorphic      10
Holomorphic curves      10
Holonomy group      65 76
Holonomy groups for principal connections      65
Holonomy Lie algebra      76
Homogeneous spaces      45
Homomorphism of G-bundles      51
Homomorphism over $\Phi$ of principal bundles      47
Horizontal bundle      37
Horizontal differential forms      63
Horizontal foliation      38
Horizontal lift      37
Horizontal projection      37
Horizontal space      32
Horizontal vectors      37
Induced connection      66 61
Inducing principal connections on associated vector bundles      69
Irreducible principle connection      66
Kinematic tangent vector      14
Lie derivation      28
Lie group      5
Linear connection      69
Linear frame bundle      52
Local description of connections      38
Local descriptions of principal connections      62
Local formulas for the Frolicher — Nijenhuis bracket      31
Manifold structure of $C^\infty(M, N)$      17
Maurer — Cartan formula      39
n-transitive      23
Natural bilinear concomitants      34
Naturality of the Frolicher — Nijenhuis bracket      33
Nearly complex structure      35
Nijenhuis tensor      35
Nijenhuis — Richardson bracket      28
Nonlinear frame bundle      81
Operational tangent vector      14
Orthonormal frame bundle      53
Orthonormal frame field      52
Parallel transport      39
Principal (fiber) bundle      44
Principal bundle atlas      44
Principal bundle of embeddings      24
Principal connection      60
Principal fiber bundle homomorphism      47
Principal right action      45
Projection      36
Proper      20
Pullback      38
Pullback of fiber bundles      37
Pullback operator      34
Real analytic      12
Real analytic curves      12
Real analytic mappings      12
Recognizing induced connections      67
Reduction of the structure group      47
Regular      23
Restricted holonomy group      65 76
Riemannian metric      52
Right logarithmic derivative      58
Sections of associated bundles      53
Self dual      99
Smooth      6 7
Smooth curves in $C^\infty(M, N)$      18
Smooth mappings      7
Smooth partitions of unity      14
Smoothness of composition      19
Space of connections      84
Standard fiber      36
Stiefel manifold      46
Tangent and vertical bundles of principal and associated bundles      58
Tangent bundles of Grassmann manifolds      56
Tangent bundles of homogeneous spaces      54
Tangent group of a Lie group      57
Tangent vectors as derivations      16
Theorem of Hartogs      10
Topologically real analytic      12
Total space      36
Transformation law for the Christoffel forms      39
Transition functions      36
Universal vector bundle      56
Vector valued differential forms      27
Vertical bundle      37
Vertical projection      37
Vertical space      32
Yang — Mills functional      100
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