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Steenrod N. — The topology of fiber bundles
Steenrod N. — The topology of fiber bundles



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Название: The topology of fiber bundles

Автор: Steenrod N.

Аннотация:

The recognition of the domain of mathematics called fibre bundles took place in the period 1935-1940. The first general definitions were given by H. Whitney. His work and that of H. Hopf and E. Stiefel demonstrated the importance of the subject for the applications of topology to differential geometry. Since then, some seventy odd papers dealing with bundles have appeared. The subject has attracted general interest, for it contains some of the finest applications of topology to other fields, and gives promise of many more. It also marks a return of algebraic topology to its origin; and, after many years of introspective development, a revitalization of the subject from its roots in the study of classical manifolds.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1951

Количество страниц: 236

Добавлена в каталог: 06.10.2012

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$C_{\sigma}$-space      50
Absolute retract      55
Admissible map      38
Associated, bundle      43
Associated, cross-section      171
Associated, map      41
Associated, translation      60
Base space      7
Boundary of a cell      100
Boundary, homomorphism      75
Bundle      13
Bundle of coefficients      151
Bundle of groups      151
Bundle of linear spaces      24
Bundle, associated      43
Bundle, induced      47
Bundle, principal      35
Bundle, product      3 16
Bundle, relative      43
Bundle, simple      17 152
Bundle, space      7
Bundle, sphere      34
Bundle, square of a      49
Bundle, sub-      24
Bundle, tangent      5 23
Bundle, tangent sphere      58
Bundle, tensor      22
Bundle, universal      101
Canonical cross-section      44
Carrier      159
Cayley numbers      108
cell      54 80 100
Cellular map      161
Chain, homomorphism      159
Chain, homotopy      159
Characteristic, class      61 66 95 178
Characteristic, class of Chern      210
Characteristic, class of Stiefel      199
Characteristic, class of Whitney      190
Characteristic, homomorphism      61 66 95
Characteristic, map      97 118 120 125
Chern characteristic classes      210
Coboundary operator      157 164
Coboundary operator of a coefficient sequence      192
Cochain      156
Cochain, deformation      172
Cochain, difference      172
Cochain, elementary      201
Cochain, homotopy      160
Cocycle      157
Cocycle, obstruction      151 166
Coefficient, bundle      151
Coefficient, group      156
Coefficient, local      155
Cohomology, group      157
Cohomology, sequence      164 191
Compact open topology      19
COMPLEX      100
Complex, analytic manifold      209
Complex, product      101
Complex, projective space      108 136
Complex, sub      100
Composition of curves      60
Connected, q-t      149
Coordinate, bundle      7
Coordinate, function      7
Coordinate, neighborhood      7
Coordinate, system      20
Coordinate, transformation      8 14
Coset space      28
Covering, homotopy      50 54
Covering, regular      70
Covering, space      5 67
Covering, transformation      70
Covering, universal      71
Cross products of chains and cochains      170
Cross-section      3
Cross-section, associated      171
Cross-section, canonical      44
Cross-section, differentiable      25
Cross-section, induced      12
Cross-section, local      30
cube      72
Deformation cochain      172
Difference cochain      172
Differentiable, cross-section      25
Differentiable, manifold      5 21
Disconnected, totally      60
Discrete      60
Effective      7
Ehresmann      18 36
Elementary cochain      201
Equivalence of coordinate bundles      8 11
Equivalence of coordinate transformations      11 15
Equivalence of fibre bundles      11
Equivalence of relative bundles      44
Equivalence, G-of bundles      17
Equivalence, homotopy      77
Equivalence, weak      99
Essential      54
Euler number      203
Exactness      76
Excision      83
Extension, homotopy      176
Extension, stepwise      148
Extension, theorems      184
Face      72 100
Factor space      28
Feldbau      18 96
Fibre      7
Fibre, bundle      9
Fibre, over x      8
Frame, k-      33
Fundamental, group      61
Fundamental, n-cycle      200
G-equivalence of bundles      17 44
G-image of a bundle      16
Graph      186
Grassmann manifold      35 134
Group of a bundle      7
Group, coefficient      156
Group, cohomology      157
Group, homotopy      73
Group, Lie      32
Group, linear      21
Group, orthogonal      33
Group, rotation      34
Group, symplectic      106 127
Group, topological      6
Group, undamental      61
Group, unitary      35 59 106 124
Homotopy, chain      159
Homotopy, classification      186
Homotopy, cochain      160
Homotopy, covering      50 54
Homotopy, equivafence      77
Homotopy, extension      176
Homotopy, group      73
Homotopy, of a bundle map      50
Homotopy, of a cross-section      167
Homotopy, relative-group      74
Homotopy, sequence      75 90
Hopf, invariant      113
Hopf, map      105
Hurewicz isomorphism      79
Image of a bundle      16
Index, Kronecker      158 200
Induced, bundle      47
Induced, cross-section      12
Induced, homomorphism of cohomology group      160
Induced, homomorphism of homotopy group      75
Induced, map      47
Inessential      54
k-field      141
k-frame      33
K-plane      142
Klein bottle      4
Kronecker index      158 200
Left translation      29
Lie group      32
Linear group      21
Local, coefficients      155
Local, cross-section      30
Manifold      20
Manifold, complex analytic      209
Manifold, differentiable      5 21
Manifold, Grassmann      35 134
Manifold, orientable      22 199
Manifold, quasi-complex      209
Manifold, Stiefel      33 132 190
Map of a bundle      9
Map, admissible      38
Map, associated      41
Map, cellular      161
Map, characteristic      97 118 120 125
Map, Hopf      105
Map, induced      47
Map, mapping transformation      10
Map, natural      28 45
Map, principal      37
Map, proper      161
Moebius band      3
Natural map      28 45
Normal form      96 119 124
Obstruction      149
Obstruction, cocycle      151 166
Obstruction, primary      178 187
Orientable, manifold      22 199
Orientable, sphere bundle      34
Orthogonal, group      33
Orthogonal, k-frame      33
Primary, difference      181
Primary, obstruction      178 187
Principal, bundle      35
Principal, map      37
Product bundle      3 16
Projection      7
Proper map      161
q-simple      87
Quadratic form      204
Quasi-complex      209
Quaternion      37 105
refinement      12
Regular covering      70
Relative, bundle      43
Relative, cohomology group      157
Relative, homotopy      75 90
Relative, homotopy group      74
retract      55
Right translation      39
Rotation group      34
Semi locally connected      64
Sequence, cohomology      164 191
Signature      204
Simple bundle      17 152
simplicity      87
Skeleton      100
Solid      54
Sphere bundle      34
Sphere bundle, orientable      34
Sphere bundle, tangent      58
Sphere bundle, unitary      210
Square of a bundle      49
Stationary      50
Stepwise extension      148
Stiefel manifolds      33 132 190
Subbundle      24
Subcomplex      100
Subdivision      161
Suspension      111 126
Symplectic group      106 127
System of coordinate transformations      14
Tangent, bundle      5 23
Tangent, sphere bundle      58
Tensor bundle      22
Topological transformation group      7
Torus      4 17
Totally disconnected      60
Translation, along a curve      59
Translation, left      29
Translation, right      39
Twisted torus      4 17
Ueberdeckung      155
Unitary, group      35 59 106 124
Unitary, sphere bundle      210
Universal, bundle      101
Universal, covering      71
Weak equivalence      99
Weakly associated      43
Whitney characteristic classes      190
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