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Steenrod N.E. — The Topology of Fibre Bundles
Steenrod N.E. — The Topology of Fibre Bundles



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Название: The Topology of Fibre Bundles

Автор: Steenrod N.E.

Аннотация:

Fibre bundles, now an integral part of differential geometry, are also of great importance in modern physics — such as in gauge theory. This book, a succinct introduction to the subject by renown mathematician Norman Steenrod, was the first to present the subject systematically.

It begins with a general introduction to bundles, including such topics as differentiable manifolds and covering spaces. The author then provides brief surveys of advanced topics, such as homotopy theory and cohomology theory, before using them to study further properties of fibre bundles. The result is a classic and timeless work of great utility that will appeal to serious mathematicians and theoretical physicists alike.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1999

Количество страниц: 224

Добавлена в каталог: 29.03.2008

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, bundle, base space      7
Associated, bundle, cross-section      171
Associated, bundle, map      41
Associated, bundle, translation      60
Boundary, homomorphism      75
Boundary, homomorphism of a cell      100
Bundle      13
Bundle, associated      43
Bundle, induced      47
Bundle, of coefficients      151
Bundle, of groups      151
Bundle, of linear spaces      24
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, homomorphism, homotopy      159
Characteristic, class      61 66 95 178
Characteristic, class, class of Chern      210
Characteristic, class, class of Stiefel      199
Characteristic, class, class of Whitney      190
Characteristic, class, homomorphism      61 66 95
Characteristic, class, 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, bundle, group      156
Coefficient, bundle, local      155
Cohomology, group      157
Cohomology, group, 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-      149
Coordinate, bundle      7
Coordinate, bundle, function      7
Coordinate, bundle, neighborhood      7
Coordinate, bundle, system      20
Coordinate, bundle, transformation      8 14
Coset space      28
Covering, homotopy      50 54
Covering, homotopy, regular      70
Covering, homotopy, space      5 67
Covering, homotopy, transformation      70
Covering, homotopy, 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, cross-section, manifold      5 21
Disconnected, totally-      60
Discrete      60
Effective      7
Ehresmann      18 36
Elementary cochain      201
Equivalence, G - of bundles      17
Equivalence, G - of bundles, homotopy      77
Equivalence, G - of bundles, of coordinate bundles      8 11
Equivalence, G - of bundles, of coordinate transformations      11 15
Equivalence, G - of bundles, of fibre bundles      11
Equivalence, G - of bundles, of relative bundles      44
Equivalence, G - of bundles, weak      99
Essential      54
Euler number      203
Exactness      76
Excision      83
Extension, homotopy      176
Extension, homotopy, stepwise      148
Extension, homotopy, 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, group, n-cycle      200
G-equivalence of bundles      17 44
G-image of a bundle      16
Graph      186
Grassmann manifold      35 134
Group, coefficient      156
Group, cohomology      157
Group, fundamental      61
Group, homotopy      73
Group, Lie      32
Group, linear      21
Group, of a bundle      7
Group, orthogonal      33
Group, rotation      34
Group, symplectic      106 127
Group, topological      6
Group, unitary      35 59 106 124
Homotopy, chain      159
Homotopy, classification      186
Homotopy, cochain      160
Homotopy, covering      50 54
Homotopy, equivalence      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, invariant, map      105
Hurewicz isomorphism      79
Image of a bundle      16
Index, Kronecker      158 200
Induced, bundle      47
Induced, bundle, cross-section      12
Induced, bundle, homomorphism of cohomology group      160
Induced, bundle, homomorphism of homotopy group      75
Induced, bundle, 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, coefficients, 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, admissible      38
Map, associated      41
Map, cellular      161
Map, characteristic      97 118 120 125
Map, Hopf      105
Map, induced      47
Map, natural      28 45
Map, of a bundle      9
Map, principal      37
Map, proper      161
Mapping transformation      10
Mobius 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, difference, obstruction      178 187
Principal, bundle      35
Principal, bundle, 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 group      74
retract      55
Right translation      39
Rotation group      34
Semi locally connected      64
Sequence, cohomology      164 191
Sequence, homotopy      75 90
Signature      204
Simple bundle      17 152
simplicity      87
Skeleton      100
Solid      54
Solid, carrier      159
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
Uberdeckung      155
Unitary, group      35 59 106 124
Unitary, sphere bundle      210
Universal, bundle      101
Universal, covering      71
Weak equivalence      99
Weakly associated      43
Whitnev characteristic classes      190
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