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Dupont J.L. — Curvature and Characteristic Classes
Dupont J.L. — Curvature and Characteristic Classes

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Название: Curvature and Characteristic Classes

Автор: Dupont J.L.

Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1978

Количество страниц: 175

Добавлена в каталог: 10.06.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Absolute neighbourhood rectract (ANR)      73
Adjoint representation      44
Alexander-Whitney map      31
Approximation to the diagonal      30
Barycentric coordinates      3
Base space of principal G-bundle      39
Bianchi identity      49
Bundle isomorphism      40
Bundle map      40
Canonical connection      94
Canonical line bundle      99
Canonical orientation of $\mathbb{C}P^1$      102
Chain, complex $C_n$      8 23
Chain, complex $C_n$ with support      9
Chain, equivalence      10
Chain, homotopy      9
Chain, map      9
Characteristic class      63 71
Chern classes      68 97
Chern polynomials, $C_k$      68
Chern — Weil homomorphism      63
Chern — Weil homomorphism for BG      94
Classifying space      71
Closed differential form      4
Cochain      8
Cochain, complex $C^n$      8 23
Cochain, complex $C^n$, with support      9
Cocycle condition      40
Complex (of modules)      12
Complex Chern — Weil homomorphism      65
Complex line bundle      99
Complex projective space      99
Complexification of a Lie group      134
Complexification of a vector bundle      104
Connection      38 46
Connection in a simplicial G-bundle      94
Continuous functor      78
Continuous natural transformation      87
Covariant derivative      58
Covariant, differential      58
Cup-product      20 30
Curvature form      49 94
De Rham cohomology      4
de Rham cohomology, complex      2
de Rham's theore for a simplicial manifold      92
de Rham's theore for a simplicial set (= Whitney's theorem)      23
de Rham's theorem      11
Degeneracy operator $\eta_i$      21
Derivation      36
Differentiable simplicial map      89
Differential form      1
Differential form on a simplicial manifold      91
Differential form on a simplicial set      22
Differential form with values in a vector space      43
Differential in a chain complex      12
Differential's in a double complex      12
distribution      52
Double complex      12
Double complex, associated to a covering      15 17
Double simplicial set      83
Edge-homomorphism      14
Elementary form $\omega_I$      25
Equivariant differential form      48
Equivariant map      39
Euler class      05 108
Euler — Poincare characteristic      10
Exact differential form      4
Excision property      9
Extension of a G-bundle      42
Exterior differential      1 44 91
Exterior product $\wedge$      1 44 91
Face map $\epsilon^i$      6
Face operator $\epsilon_i$      7 21
Fat realization      75
Fibre bundle      42
Fibre bundle of principal G-bundle      39
filling      146 163
Flat bundle      144
Flat connection      47 51
Foliation      52
Frame bundle      38
Free G-action      72
Fundamental class      111
Gauss — Bonnet formula      112
Geodesic simplex      150
Geodesically convex      11
Geometric realization      75
Graded commutative      1
Group cohomology      145
Hirzebruch proportionality principle      161
Homotopy of $C^{\infty}$ maps      9
Homotopy of simplicial maps      35
Homotopy property      9
Hopf bundle      99
Hopf's formula      109
Horizontal differential form      48
Horizontal tangent vectors      38 46
Induced bundle (= "pull-back")      41
Induced differential form      2
Integration      6 112
Integration along a manifold      22
Integration map, I      10 23 92
Integration operators, $h_{(i)}$      4 7
Invariant differential form      48
Invariant polynomial      62
Jordan-decomposition      135
Levi-Civita connection      56
Local index of vector field      109
Local trivialization      40 42
Maurer — Cartan connection      47
Maximal torus      115
Natural transformation      10
Nerve      77
Nerve of a covering, $NX_U$      79
Nilpotent element      135
Normal cochain      35
Normal neighbourhood      11
Normal simplicial k-form      36
Oriented vector bundle      108
Orthonormal frame bundle      43
Parallel translation      38
Pfaffian polynomial      66
Poincare's lemma      4
Poincare's upper halfplane      161
Polarization      62
Polynomial form      37
Polynomial function      62
Pontrjagin classes      66 103
Pontrjagin polynomials      66
Positive root      137
Principal $\Gamma$-covering      159
Principal G-bundle      39
Rational differential form      37
Realification      106
Reduction of a G-bundle      42
Regular element      128
Relative Euler class      108
Root      137
Root space decomposition      126
Semi-simple element      135
Simplicial chain complex      23
Simplicial cochain complex      23
Simplicial de Rham complex      20 91
Simplicial form      22
Simplicial G-bundle      93
Simplicial homotopy      35
Simplicial manifold      89
Simplicial map      21
Simplicial set      21
Simplicial space      75
Singular boundary operator      8
Singular chain      8
Singular coboundary operator      8
Singular cochain      8
Singular cohomology      8
Singular element in a L i e algebra      42
Singular homology      8
Singular simplex      7
Skew-Hermitian matrix      68
Standard simplex      3
Star-shaped set      4
Stoke's theorem      6
Strongly free G-action      72
Structural equation      49
Symmetric algebra      69
Symmetric multilinear function      61
Symmetric power      69
Symplectic group      52
Tensor algebra      68
Tensor property      1
Thom class      108
Topological category      77
Topological principal G-bundle      71
Torsion-form      55
Torus      117
Total Chern class      99
Total complex      12
Total Pontrjagin class      104
Total space of principal G-bundle      39
Transition functions      40
Trivial bundle      40
Vertical tangent vectors      45
Weyl group      115
Whitney duality formula      100 105 110
Whitney sum      98
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