Главная    Ex Libris    Книги    Журналы    Статьи    Серии    Каталог    Wanted    Загрузка    ХудЛит    Справка    Поиск по индексам    Поиск    Форум   
blank
Авторизация

       
blank
Поиск по указателям

blank
blank
blank
Красота
blank
Husemoller D. — Fibre Bundles
Husemoller D. — Fibre Bundles



Обсудите книгу на научном форуме



Нашли опечатку?
Выделите ее мышкой и нажмите Ctrl+Enter

Название: Fibre Bundles

Автор: Husemoller D.

Аннотация:

Fibre bundles play an important role in just about every aspect of modern geometry and topology. Basic properties, homotopy classification, and characteristic classes of fibre bundles have become an essential part of graduate mathematical education for students in geometry and mathematical physics. In this third edition two new chapters on the gauge group of a bundle and on the differential forms representing characteristic classes of complex vector bundles on manifolds have been added. These chapters result from the important role of the gauge group in mathematical physics and the continual usefulness of characteristic classes defined with connections on vector bundles.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: 3rd Edition

Год издания: 1993

Количество страниц: 380

Добавлена в каталог: 22.05.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
blank
Предметный указатель
$\lambda$-ring(s)      171
$\lambda$-ring(s), $\gamma$-operations in      175
$\lambda$-ring(s), Adams operations in      172
$\lambda$-ring(s), K(X) and KO(X) as      171 186—188
$\lambda$-ring(s), representation ring as      180 181 185
$\lambda$-ring(s), split      174
$\tilde{K}(X)$ and $\widetilde{KO}(X)$      114—117
$\tilde{K}(X)$ and $\widetilde{KO}(X)$, calculation of $\tilde{K}(S^n)$      187 188
$\tilde{K}(X)$ and $\widetilde{KO}(X)$, corepresentation of      118 119
$\tilde{K}(X)$ and $\widetilde{KO}(X)$, table of results for $\widetilde{KO}(S^n)$ and $\widetilde{KO}(RP^n)$      235—237
Adams conjecture      240
Adams operations      172
Adams operations, in $\lambda$-rings      172—174
Adams operations, on real spin representations      207 238
Alexander duality theorem      271
Atiyah duality theorem      221 222
Atlas of charts, for fibre bundle      62
Atlas of charts, for fibre bundle, for manifold      263
Automorphisms of principal bundles      79—81
Base space      11
Bianchi identity      287
Bilinear form, symmetric      154
Bott periodicity      140 149
Bott periodicity, and integrality theorem      150 236 307 308
Bundle(s)      11
Bundle(s), collapsed      122
Bundle(s), fibre product of      16
Bundle(s), G-      42
Bundle(s), Hopf      141
Bundle(s), induced      18
Bundle(s), locally isomorphic      20
Bundle(s), locally trivial      20
Bundle(s), morphism of      14
Bundle(s), product of      15
Bundle(s), restricted      17
Bundle(s), sub-      11
Bundle(s), sub-, tangent      see “Tangent bundle”
Character ring      180
Character ring, representation ring as      180 181
Characteristic classes      295 296 300 304
Characteristic classes and representations      309—311
Characteristic classes, calculations, on canonical line bundles      248 249 259—261
Characteristic classes, calculations, on canonical line bundles, on tangent bundles of $S^n$, $RP^n$, and $CP^n$      250 251 306 307
Characteristic classes, complex      297—299
Characteristic classes, complex, in dimension n      296 298
Characteristic classes, real, mod 2      300—301
Characteristic classes, real, mod 2, 2-divisible      301—304
Characteristic map      101—104
Charts, of fibre bundles      62
Charts, of fibre bundles, of manifolds      263
Charts, of fibre bundles, of vector bundles      24 62
Chern classes      249 296—299
Chern classes, axiomatic properties of      249
Chern classes, definition      249
Chern classes, multiplicative property of      252
Chern forms      286
Chern forms, curvature      284 285
Chern forms, definition      284
Chern forms, homotopy formula      288—291
Chern — Simons invariants      290 291
Classical groups      87—90
Classical groups, classifying spaces for      95 96
Classical groups, examples      89 90
Classical groups, homotopy groups of      95 104—107
Classical groups, infinite      88
Classical groups, stability of      94 95
Classical groups, universal bundle for      95 96
Classifying spaces      63
Classifying spaces, cohomology of      297 300 302
Classifying spaces, for classical groups      95 96
Classifying spaces, of reduced structure group      77
Classifying spaces, of vector bundles      31 32 96
Clifford algebras      156—161
Clifford algebras, calculations of      158
Clifford algebras, table      161
Clifford modules      161—163
Clifford modules, table      163
Clifford modules, tensor products of      166—168
Clutching construction      134—136
Clutching maps      135
Clutching maps, Laurent      142
Clutching maps, linear      145—148
Clutching maps, polynomial      143—145
Cobordism      276—278
coH-space      7
Cokernel of morphism      35—37
Collapsed bundle      122
Compact group      179
Compact group, maximal tori of      182—184
Compact group, rank of      183
Compact group, representation ring of      179—181
Compact group, Weyl group of      184
Compact-open topology      4
Cone over a space      5
Connections on a vector bundle      
Coreducible spaces      228
Coreducible spaces, relation to vector fields      179—181
Covariant derivative      292
Cross section(s)      12
Cross section(s), and Euler class      257
Cross section(s), of fibre bundles      48
Cross section(s), prolongation of      21
CW-complex(es)      2
CW-complex(es), homotopy classification over      58
De Rham cohomology      281
Difference isomorphism      131—133
Differential forms      280—283
Duality theorem, Poincare      271
Duality, in manifolds      269—272
Eilenberg — MacLane spaces      83—86
Euclidean inner product      12
Euclidean norm      12
Euclidean space, orientation in      266—267
Euler characteristic, definition      274—275
Euler characteristic, definition, and Euler class      274—275
Euler characteristic, definition, and vector fields      275
Euler characteristic, definition, of stable vector bundles      137
Euler class      254 301—303
Euler class, and cross sections      257
Euler class, and Euler characteristic      274 275
Euler class, and Thorn isomorphism      258
Euler class, definition      254
Euler class, multiplicative property      256 257
Euler class, of a manifold      274 275
Fibre      11
Fibre bundle(s)      45
Fibre bundle(s), atlas of charts for      62
Fibre bundle(s), automorphisms      61 79—81
Fibre bundle(s), classification of      56—59
Fibre bundle(s), cross section of      48
Fibre bundle(s), locally trivial      47
Fibre bundle(s), morphism of      46
Fibre bundle(s), over suspension      85
Fibre bundle(s), trivial      47
Fibre homotopy equivalence      223 224 312 313
Fibre homotopy type      223 224 312 317
Fibre homotopy type and Thorn spaces      227 228
Fibre homotopy type, stable      223—228
Fibre maps      7 312—313
Fibre product      16
Fibre, of a fibre bundle      45
Fibre, of a principal bundle      43
G-module      176
G-module, direct sum of      176
G-module, exterior product of      176
G-module, morphism of      176
G-module, semisimple      177 179
G-module, tensor product of      176
G-space      40
G-space, morphism of      41
G-space, principal      42
Gauge group, calculation of      81
Gauge group, classifying space of      83
Gauge group, definiton      79—81
Gauge group, universal bundle of      83
Gauss map      33
Grassman manifold (or variety)      13 25 34
Grassman manifold (or variety), as homogeneous space      90 91
Grassman manifold (or variety), cohomology of      297 300 302
Group(s), linear      40
Group(s), reduction of structure      77
Group(s), topological      40
Group(s), transformation      40
Gysin sequence      255
H-space      6
Half-exact cofunctor      138
Half-exact cofunctor, Puppe sequence of      139
Hermitian metrics of vector bundle      37
Homotopy classification, over CW-complexes      58
Homotopy classification, over CW-complexes, of principal bundles      56—58
Homotopy classification, over CW-complexes, of vector bundle      33—35 113 114
Homotopy equivalence      1
Homotopy equivalence, fibre      223 224 285 312 313
Homotopy formula for connections      288—291
Homotopy formula for differential forms      283
Homotopy groups      7
Homotopy groups, of classical groups      94 104—107
Homotopy groups, of O(n)      94 104—107
Homotopy groups, of SO(n)      94 104—107
Homotopy groups, of Sp(n)      94 104—107
Homotopy groups, of Stiefel variety      95 103 104
Homotopy groups, of SU(n)      94 104—107
Homotopy groups, of U(n)      94 104—107
Hopf bundle      142 143
Hopf invariant      210—216 309 326—328
Integrality theorem of Bott      307 308
J(X)      224
J(X), calculation of $J(RP^n)$      237—239
J(X), calculation of $J(S^k)$      225—227
K(X) and KO(X)      114—117 120
K(X) and KO(X), and representation ring      180—181
K(X) and KO(X), as $\lambda$-ring      171 186—188
K(X) and KO(X), as a ring      128
K(X) and KO(X), Bott periodicity of      140 148—150 236
K-cup product      128
k-space      2
Kunneth formula      85 86
Leray — Hirsch theorem      245
Levi — Civita, connection      291—293
Linear groups      40
Loop space      5
Manifold(s)      262—279
Manifold(s), atlas of charts for      262 263
Manifold(s), duality in      269—272
Manifold(s), Euler class of      274
Manifold(s), fundamental class of      268
Manifold(s), Grassman      see “Grassman manifold (or variety)”
Manifold(s), orientation of      267—269
Manifold(s), Stiefel — Whitney classes of      275 276
Manifold(s), tangent bundle to      264
Manifold(s), Thorn class of      272—274
Map space      4
Map(s), fibre      7 312 313
Map(s), Gauss      33
Map(s), normal bundle of      265
Map(s), splitting      251
Mapping cone      125
Mapping cylinder      125
Maximal tori, of compact groups      182—184
Maximal tori, of compact groups, of SO(n)      195 196
Maximal tori, of compact groups, of Sp(n)      193
Maximal tori, of compact groups, of Spin(n)      196 197
Maximal tori, of compact groups, of SU(n)      191
Maximal tori, of compact groups, of U(n)      191
Mayer — Vietoris sequence      246 268—270
Milnor's construction of a universal bundle      54—56
Milnor's construction of a universal bundle, verification of universal property      56—58
Morphism, B-      14
Morphism, cokernel of      36
Morphism, image of      36
Morphism, kernel of      36
Morphism, local representation of      66
Morphism, of bundles      14
Morphism, of fibre bundles      45
Morphism, of G-module      176
Morphism, of G-space      42
Morphism, of principal bundles      43
Morphism, of vector bundles      26
Normal bundle, of an immersion      278
Normal bundle, of an immersion, of a map      265
Normal bundle, of an immersion, to the sphere      13
Numerable covering      49 312
Orientation class      267 268
Orientation, in euclidean space      266 267
Orientation, in euclidean space, of manifolds      267—269
Orientation, in euclidean space, of vector bundles      260
Orthogonal group (O(n)) and (SO(n))      40 87
Orthogonal group (O(n)) and (SO(n)) examples      90
Orthogonal group (O(n)) and (SO(n)) homotopy groups of      94 104—107
Orthogonal group (O(n)) and (SO(n)) infinite      88
Orthogonal group (O(n)) and (SO(n)) maximal tori of      195 196
Orthogonal group (O(n)) and (SO(n)) representation ring of      200—203
Orthogonal group (O(n)) and (SO(n)) Weyl group of      195 196
Orthogonal multiplication      152 153
Orthogonal splitting      155 156
Path space      5
Poincare duality theorem      271
Pontrjagin classes      259 260 301—304
Principal bundle(s)      42
Principal bundle(s), homotopy classification of      56—58
Principal bundle(s), induced      43
Principal bundle(s), morphism of      42
Principal bundle(s), numerable      49
Products, of bundles      15—17
Products, of bundles, euclidean inner      13
Products, of bundles, of G-module, exterior      176
Products, of bundles, of G-module, tensor      176
Products, of bundles, reduced      5
Projection      11
Projective space      2
Projective space, tangent bundle of      14 17 251
Puppe sequence      125—127 139 220 221
Quadratic form      154
Rank of a compact group      183
Reduced product      5
Reducible spaces      227
Reducible spaces, relation to vector fields      230—232
Representation ring      177—178 203—205
Representation ring, as $\lambda$-ring      177 178 186 187
Representation ring, character ring as      180 181
Representation ring, K(X) and KO(X) and      177 178
Representation ring, of a torus      185 186
Representation ring, of compact group      179—181
Representation ring, of SO(n)      200—203
Representation ring, of Sp(n)      195
Representation ring, of Spin(w)      200—203
Representation ring, of SU(n)      192
Representation ring, of U(n)      192
Representation ring, real      203—206
Representation ring, real-Spin      203—205
Representation(s)      176—178
Representation(s), and characteristic classes      309—311
Representation(s), and vector bundles      177—178
Representation(s), local, of morphism      66
Representation(s), real, of Spin(w)      203—205
Representation(s), semisimple      179 180
Riemann connection      291—293
Riemannian metrics of vector bundle      37 38
S-category      219—220
Schur's lemma      179
1 2
blank
Реклама
blank
blank
HR
@Mail.ru
       © Электронная библиотека попечительского совета мехмата МГУ, 2004-2024
Электронная библиотека мехмата МГУ | Valid HTML 4.01! | Valid CSS! О проекте