Fibre bundles:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York u.a.
Springer
1975
|
| Ausgabe: | 2. ed. |
| Schriftenreihe: | Graduate texts in mathematics.
20. |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis Inhaltsverzeichnis |
| Beschreibung: | XV, 327 S. graph. Darst. |
| ISBN: | 0387901035 3540901035 |
Internformat
MARC
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| 100 | 1 | |a Husemöller, Dale |e Verfasser |0 (DE-588)117713058 |4 aut | |
| 245 | 1 | 0 | |a Fibre bundles |c Dale Husemöller |
| 250 | |a 2. ed. | ||
| 264 | 1 | |a New York u.a. |b Springer |c 1975 | |
| 300 | |a XV, 327 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Graduate texts in mathematics. |v 20. | |
| 650 | 7 | |a Differentiaalmeetkunde |2 gtt | |
| 650 | 4 | |a Faisceaux fibrés (Mathématiques) | |
| 650 | 7 | |a Vezels (wiskunde) |2 gtt | |
| 650 | 4 | |a Fiber bundles (Mathematics) | |
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Datensatz im Suchindex
| _version_ | 1804116406003826688 |
|---|---|
| adam_text | CONTENTS
PREFACE vii
1
PRELIMINARIES ON HOMOTOPY THEORY 1
1. Category theory and homotopy theory 1
2. Complexes 2
3. The spaces Map (X, Y) and Map0 (X, Y) 4
4. Homotopy groups of spaces 6
5. Fibre maps 7
PART I
THE GENERAL THEORY OF FIBRE BUNDLES
2
GENERALITIES ON BUNDLES 11
1. Definition of bundles and cross sections 11
2. Examples of bundles and cross sections 12
3. Morphisms of bundles 14
4. Products and fibre products 15
5. Restrictions of bundles and induced bundles 17
6. Local properties of bundles 20
7. Prolongation of cross sections 20
Exercises 22
3
VECTOR BUNDLES 23
1. Definition and examples of vector bundles 23
2. Morphisms of vector bundles 25
ix
x Contents
3. Induced vector bundles 26
4. Homotopy properties of vector bundles 27
5. Construction of Gauss maps 29
6. Homotopies of Gauss maps 31
7. Functorial description of the homotopy classification of vector bundles 32
8. Kernel, image, and cokernel of morphisms with constant rank 34
9. Riemannian and Hermitian metrics on vector bundles 35
Exercises 37
4
GENERAL FIBRE BUNDLES 39
1. Bundles defined by transformation groups 39
2. Definition and examples of principal bundles 40
3. Categories of principal bundles 41
4. Induced bundles of principal bundles 42
5. Definition of fibre bundles 43
6. Functorial properties of fibre bundles 45
7. Trivial and locally trivial fibre bundles 46
8. Description of cross sections of a fibre bundle 46
9. Numerable principal bundles over B X [0, 1] 48
10. The cofunctor ka 51
11. The Milnor construction 52
12. Homotopy classification of numerable principal G-bundles 54
13. Homotopy classification of principal G- bundles over CW- complexes 57
Exercises 57
5
LOCAL COORDINATE DESCRIPTION OF FIBRE BUNDLES 59
1. Automorphisms of trivial fibre bundles 59
2. Charts and transition functions 60
3. Construction of bundles with given transition functions 62
4. Transition functions and induced bundles 63
5. Local representation of vector bundle morphisms 64
6. Operations on vector bundles 65
7. Transition functions for bundles with metrics 67
Exercises 69
6
CHANGE OF STRUCTURE GROUP IN FIBRF BUNDLES 70
1. Fibre bundles with homogeneous spaces as fibres 70
2. Prolongation and restriction of principal bundles 71
3. Restriction and prolongation of structure group for fibre bundles 72
4. Local coordinate description of change of structure group 73
Contents xi
5. Classifying spaces and the reduction of structure group 73
Exercises 74
7
CALCULATIONS INVOLVING THE CLASSICAL GROUPS 75
1. Stiefel varieties and the classical groups 75
2. Grassmann manifolds and the classical groups 78
3. Local triviality of projections from Stiefel varieties 79
4. Stability of the homotopy groups of the classical groups 82
5. Vanishing of lower homotopy groups of Stiefel varieties 83
6. Universal bundles and classifying spaces for the classical groups 83
7. Universal vector bundles 84
8. Description of all locally trivial fibre bundles over suspensions 85
9. Characteristic map of the tangent bundle over S 86
10. Homotopy properties of characteristic maps 89
11. Homotopy groups of Stiefel varieties 91
12. Some of the homotopy groups of the classical groups 92
Exercises 95
PART II
ELEMENTS OF JC THEORY
8
STABILITY PROPERTIES OF VECTOR BUNDLES 99
1. Trivial summands of vector bundles 99
2. Homotopy classification and Whitney sums 100
3. The K cofunctors 102
4. Corepresentations of Kr 105
5. Homotopy groups of classical groups and Kf(S ) 108
Exercises 109
9
RELATIVE K-THEORY 110
1. Collapsing of trivialized bundles 110
2. Exact sequences in relative if-theory 112
3. Products in K-theory 116
4. The cofunctor L(X, A) 117
5. The difference morphism 119
6. Products in L(X, A) 121
7. The clutching construction 122
8. The cofunctor Ln{X, A) 124
9. Half-exact cofunctors 126
Exercises 127
xii Contents
10
BOTT PERIODICITY IN THE COMPLEX CASE 128
1. if-theory interpretation of the periodicity result 128
2. Complex vector bundles over X X S2 129
3. Analysis of polynomial clutching maps 131
4. Analysis of linear clutching maps 133
5. The inverse to the periodicity isomorphism 136
11
CLIFFORD ALGEBRAS 139
1. Unit tangent vector fields on spheres: I 139
2. Orthogonal multiplications 140
3. Generalities on quadratic forms 141
4. Clifford algebra of a quadratic form 144
5. Calculations of Clifford algebras 146
6. Clifford modules 149
7. Tensor products of Clifford modules 154
8. Unit tangent vector fields on spheres: II 156
9. The group Spin(fc) 157
Exercises 158
12
THE ADAMS OPERATIONS AND REPRESENTATIONS 159
1. X-rings 159
2. The Adams ^--operations in X-ring 160
3. The 7* operations 162
4. Generalities on G-modules 163
5. The representation ring of a group G and vector bundles 165
6. Semisimplicity of G-modules over compact groups 166
7. Characters and the structure of the group Rf(G) 168
8. Maximal tori 169
9. The representation ring of a torus 172
10. The ^-operations on K(X) and K0(X) 173
11. The ^-operations on K(Sn) 175
13
REPRESENTATION RINGS OF CLASSICAL GROUPS 176
1. Symmetric functions 176
2. Maximal tori in SU(n) and U(n) 178
3. The representation rings of SU(n) and V(n) 179
4. Maximal tori in Sp(ra) 180
5. Formal identities in polynomial rings 180
6. The representation ring of Sp(n) 181
Contents xiii
7. Maximal tori and the Weyl group of SO(n) 182
8. Maximal tori and the Weyl group of Spin(n) 183
9. Special representations of SO(n) and Spin(n) 184
10. Calculation of RSO(n) and flSpin(n) 187
11. Relation between real and complex representation rings 190
12. Examples of real and quaternionic representations 193
13. Spinor representations and the if-groups of spheres 195
14
THE HOPF INVARIANT 196
1. K-theory definition of the Hopf invariant 196
2. Algebraic properties of the Hopf invariant 197
3. Hopf invariant and bidegree 199
4. Nonexistence of elements of Hopf invariant 1 201
15
VECTOR FIELDS ON THE SPHERE AND STABLE
HOMOTOPY 203
1. Thorn spaces of vector bundles 203
2. S-category 205
3. S-duality and the Atiyah duality theorem 207
4. Fibre homotopy type 208
5. Stable fibre homotopy equivalence 210
6. The groups J(S ) and KtoB(S ) 211
7. Thom spaces and fibre homotopy type 213
8. S-duality and S-reducibility 215
9. Nonexistence of vector fields and reducibility 216
10. Nonexistence of vector fields and coreducibility 218
11. Nonexistence of vector fields and J(RPk) 219
12. Real if-groups of real projective spaces 222
13. Relation between K0(RP ) and J(RP ) 223
14. Remarks on the Adams conjecture 226
PART HI
CHARACTERISTIC CLASSES
16
CHERN CLASSES AND STIEFEL-WHITNEY CLASSES 231
1. The Leray-Hirsch theorem 231
2. Definition of the Stiefel-Whitney classes and Chern classes 232
3. Axiomatic properties of the characteristic classes 234
4. Stability properties and examples of characteristic classes 236
5. Splitting maps and uniqueness of characteristic classes 237
6. Existence of the characteristic classes 238
xiv Contents
7. Fundamental class of sphere bundles. Gysin sequence 239
8. Multiplicative property of the Euler class 241
9. Definition of Stiefel-Whitney classes using the squaring operations of
Steenrod 243
10. The Thorn isomorphism 243
11. Relations between real and complex vector bundles 244
12. Orientability and Stiefel-Whitney classes 246
Exercises 246
17
DIFFERENTIABLE MANIFOLDS 248
1. Generalities on manifolds 248
2. The tangent bundle to a manifold 250
3. Orientation in euclidean spaces 251
4. Orientation of manifolds 253
5. Duality in manifolds 255
6. Thorn class of the tangent bundle 257
7. Euler characteristic and class of a manifold 259
8. Wu s formula for the Stiefel-Whitney class of a manifold 261
9. Stiefel-Whitney numbers and cobordism 262
10. Immersions and embeddings of manifolds 263
Exercises 264
18
GENERAL THEORY OF CHARACTERISTIC CLASSES 266
1. The Yoneda representation theorem 266
2. Generalities on characteristic classes 267
3. Complex characteristic classes in dimension n 268
4. Complex characteristic classes 269
5. Real characteristic classes mod 2 271
6. 2-divisible real characteristic classes in dimension n 273
7. Oriented even-dimensional real characteristic classes 276
8. Examples and applications 278
9. Bott periodicity and integrality theorems 279
10. Comparison of it-theory and cohomology definitions of Hopf invariant 280
11. The Borel-Hirzebruch description of characteristic classes 281
appendix 1: Dold s theory of local properties of bundles 285
appendix 2: On the double suspension 287
1. H,(aS(X)) as an algebraic functor of Ht(X) 288
2. Connectivity of the pair (n2S2 +1, S2 1) localized at p 291
3. Decomposition of suspensions of products and 0S(X) 292
4. Single suspension sequences 295
Contents xv
5. Mod p Hopf invariant 299
6. Spaces where the pth power is zero 302
7. Double suspension sequences 306
8. Study of the boundary map A: n3S2 +1 - QS2 1 309
bibliography 313
index 323
CONTENTS
PREFACE vii
1
PRELIMINARIES ON HOMOTOPY THEORY 1
1. Category theory and homotopy theory 1
2. Complexes 2
3. The spaces Map (X, Y) and Map0 (X, Y) 4
4. Homotopy groups of spaces 6
5. Fibre maps 7
PART I
THE GENERAL THEORY OF FIBRE BUNDLES
2
GENERALITIES ON BUNDLES 11
1. Definition of bundles and cross sections 11
2. Examples of bundles and cross sections 12
3. Morphisms of bundles 14
4. Products and fibre products 15
5. Restrictions of bundles and induced bundles 17
6. Local properties of bundles 20
7. Prolongation of cross sections 20
Exercises 22
3
VECTOR BUNDLES 23
1. Definition and examples of vector bundles 23
2. Morphisms of vector bundles 25
ix
x Contents
3. Induced vector bundles 26
4. Homotopy properties of vector bundles 27
5. Construction of Gauss maps 29
6. Homotopies of Gauss maps 31
7. Functorial description of the homotopy classification of vector bundles 32
8. Kernel, image, and cokernel of morphisms with constant rank 34
9. Riemannian and Hermitian metrics on vector bundles 35
Exercises 37
4
GENERAL FIBRE BUNDLES 39
1. Bundles defined by transformation groups 39
2. Definition and examples of principal bundles 40
3. Categories of principal bundles 41
4. Induced bundles of principal bundles 42
5. Definition of fibre bundles 43
6. Functorial properties of fibre bundles 45
7. Trivial and locally trivial fibre bundles 46
8. Description of cross sections of a fibre bundle 46
9. Numerable principal bundles over B X [0, 1] 48
10. The cofunctor ka 51
11. The Milnor construction 52
12. Homotopy classification of numerable principal G bundles 54
13. Homotopy classification of principal G bundles over CW complexes 57
Exercises 57
5
LOCAL COORDINATE DESCRIPTION OF FIBRE BUNDLES 59
1. Automorphisms of trivial fibre bundles 59
2. Charts and transition functions 60
3. Construction of bundles with given transition functions 62
4. Transition functions and induced bundles 63
5. Local representation of vector bundle morphisms 64
6. Operations on vector bundles 65
7. Transition functions for bundles with metrics 67
Exercises 69
6
CHANGE OF STRUCTURE GROUP IN FIBRF BUNDLES 70
1. Fibre bundles with homogeneous spaces as fibres 70
2. Prolongation and restriction of principal bundles 71
3. Restriction and prolongation of structure group for fibre bundles 72
4. Local coordinate description of change of structure group 73
Contents xi
5. Classifying spaces and the reduction of structure group 73
Exercises 74
7
CALCULATIONS INVOLVING THE CLASSICAL GROUPS 75
1. Stiefel varieties and the classical groups 75
2. Grassmann manifolds and the classical groups 78
3. Local triviality of projections from Stiefel varieties 79
4. Stability of the homotopy groups of the classical groups 82
5. Vanishing of lower homotopy groups of Stiefel varieties 83
6. Universal bundles and classifying spaces for the classical groups 83
7. Universal vector bundles 84
8. Description of all locally trivial fibre bundles over suspensions 85
9. Characteristic map of the tangent bundle over S 86
10. Homotopy properties of characteristic maps 89
11. Homotopy groups of Stiefel varieties 91
12. Some of the homotopy groups of the classical groups 92
Exercises 95
PART II
ELEMENTS OF JC THEORY
8
STABILITY PROPERTIES OF VECTOR BUNDLES 99
1. Trivial summands of vector bundles 99
2. Homotopy classification and Whitney sums 100
3. The K cofunctors 102
4. Corepresentations of Kr 105
5. Homotopy groups of classical groups and Kf(S ) 108
Exercises 109
9
RELATIVE K THEORY 110
1. Collapsing of trivialized bundles 110
2. Exact sequences in relative if theory 112
3. Products in K theory 116
4. The cofunctor L(X, A) 117
5. The difference morphism 119
6. Products in L(X, A) 121
7. The clutching construction 122
8. The cofunctor Ln{X, A) 124
9. Half exact cofunctors 126
Exercises 127
xii Contents
10
BOTT PERIODICITY IN THE COMPLEX CASE 128
1. if theory interpretation of the periodicity result 128
2. Complex vector bundles over X X S2 129
3. Analysis of polynomial clutching maps 131
4. Analysis of linear clutching maps 133
5. The inverse to the periodicity isomorphism 136
11
CLIFFORD ALGEBRAS 139
1. Unit tangent vector fields on spheres: I 139
2. Orthogonal multiplications 140
3. Generalities on quadratic forms 141
4. Clifford algebra of a quadratic form 144
5. Calculations of Clifford algebras 146
6. Clifford modules 149
7. Tensor products of Clifford modules 154
8. Unit tangent vector fields on spheres: II 156
9. The group Spin(fc) 157
Exercises 158
12
THE ADAMS OPERATIONS AND REPRESENTATIONS 159
1. X rings 159
2. The Adams ^ operations in X ring 160
3. The 7* operations 162
4. Generalities on G modules 163
5. The representation ring of a group G and vector bundles 165
6. Semisimplicity of G modules over compact groups 166
7. Characters and the structure of the group Rf(G) 168
8. Maximal tori 169
9. The representation ring of a torus 172
10. The ^ operations on K(X) and K0(X) 173
11. The ^ operations on K(Sn) 175
13
REPRESENTATION RINGS OF CLASSICAL GROUPS 176
1. Symmetric functions 176
2. Maximal tori in SU(n) and U(n) 178
3. The representation rings of SU(n) and V(n) 179
4. Maximal tori in Sp(ra) 180
5. Formal identities in polynomial rings 180
6. The representation ring of Sp(n) 181
Contents xiii
7. Maximal tori and the Weyl group of SO(n) 182
8. Maximal tori and the Weyl group of Spin(n) 183
9. Special representations of SO(n) and Spin(n) 184
10. Calculation of RSO(n) and flSpin(n) 187
11. Relation between real and complex representation rings 190
12. Examples of real and quaternionic representations 193
13. Spinor representations and the if groups of spheres 195
14
THE HOPF INVARIANT 196
1. K theory definition of the Hopf invariant 196
2. Algebraic properties of the Hopf invariant 197
3. Hopf invariant and bidegree 199
4. Nonexistence of elements of Hopf invariant 1 201
15
VECTOR FIELDS ON THE SPHERE AND STABLE
HOMOTOPY 203
1. Thorn spaces of vector bundles 203
2. S category 205
3. S duality and the Atiyah duality theorem 207
4. Fibre homotopy type 208
5. Stable fibre homotopy equivalence 210
6. The groups J(S ) and KtoB(S ) 211
7. Thom spaces and fibre homotopy type 213
8. S duality and S reducibility 215
9. Nonexistence of vector fields and reducibility 216
10. Nonexistence of vector fields and coreducibility 218
11. Nonexistence of vector fields and J(RPk) 219
12. Real if groups of real projective spaces 222
13. Relation between K0(RP ) and J(RP ) 223
14. Remarks on the Adams conjecture 226
PART HI
CHARACTERISTIC CLASSES
16
CHERN CLASSES AND STIEFEL WHITNEY CLASSES 231
1. The Leray Hirsch theorem 231
2. Definition of the Stiefel Whitney classes and Chern classes 232
3. Axiomatic properties of the characteristic classes 234
4. Stability properties and examples of characteristic classes 236
5. Splitting maps and uniqueness of characteristic classes 237
6. Existence of the characteristic classes 238
xiv Contents
7. Fundamental class of sphere bundles. Gysin sequence 239
8. Multiplicative property of the Euler class 241
9. Definition of Stiefel Whitney classes using the squaring operations of
Steenrod 243
10. The Thorn isomorphism 243
11. Relations between real and complex vector bundles 244
12. Orientability and Stiefel Whitney classes 246
Exercises 246
17
DIFFERENTIABLE MANIFOLDS 248
1. Generalities on manifolds 248
2. The tangent bundle to a manifold 250
3. Orientation in euclidean spaces 251
4. Orientation of manifolds 253
5. Duality in manifolds 255
6. Thorn class of the tangent bundle 257
7. Euler characteristic and class of a manifold 259
8. Wu s formula for the Stiefel Whitney class of a manifold 261
9. Stiefel Whitney numbers and cobordism 262
10. Immersions and embeddings of manifolds 263
Exercises 264
18
GENERAL THEORY OF CHARACTERISTIC CLASSES 266
1. The Yoneda representation theorem 266
2. Generalities on characteristic classes 267
3. Complex characteristic classes in dimension n 268
4. Complex characteristic classes 269
5. Real characteristic classes mod 2 271
6. 2 divisible real characteristic classes in dimension n 273
7. Oriented even dimensional real characteristic classes 276
8. Examples and applications 278
9. Bott periodicity and integrality theorems 279
10. Comparison of it theory and cohomology definitions of Hopf invariant 280
11. The Borel Hirzebruch description of characteristic classes 281
appendix 1: Dold s theory of local properties of bundles 285
appendix 2: On the double suspension 287
1. H,(aS(X)) as an algebraic functor of Ht(X) 288
2. Connectivity of the pair (n2S2 +1, S2 1) localized at p 291
3. Decomposition of suspensions of products and 0S(X) 292
4. Single suspension sequences 295
Contents xv
5. Mod p Hopf invariant 299
6. Spaces where the pth power is zero 302
7. Double suspension sequences 306
8. Study of the boundary map A: n3S2 +1 QS2 1 309
bibliography 313
index 323
|
| any_adam_object | 1 |
| author | Husemöller, Dale |
| author_GND | (DE-588)117713058 |
| author_facet | Husemöller, Dale |
| author_role | aut |
| author_sort | Husemöller, Dale |
| author_variant | d h dh |
| building | Verbundindex |
| bvnumber | BV001963010 |
| callnumber-first | Q - Science |
| callnumber-label | QA612 |
| callnumber-raw | QA612.6 |
| callnumber-search | QA612.6 |
| callnumber-sort | QA 3612.6 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 300 SK 350 |
| ctrlnum | (OCoLC)1093485 (DE-599)BVBBV001963010 |
| dewey-full | 514/.224 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 514 - Topology |
| dewey-raw | 514/.224 |
| dewey-search | 514/.224 |
| dewey-sort | 3514 3224 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 2. ed. |
| format | Book |
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| genre | (DE-588)4151278-9 Einführung gnd-content |
| genre_facet | Einführung |
| id | DE-604.BV001963010 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T15:38:00Z |
| institution | BVB |
| isbn | 0387901035 3540901035 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-001280184 |
| oclc_num | 1093485 |
| open_access_boolean | |
| owner | DE-91G DE-BY-TUM DE-384 DE-473 DE-BY-UBG DE-739 DE-29T DE-19 DE-BY-UBM DE-703 DE-824 DE-83 DE-188 DE-706 |
| owner_facet | DE-91G DE-BY-TUM DE-384 DE-473 DE-BY-UBG DE-739 DE-29T DE-19 DE-BY-UBM DE-703 DE-824 DE-83 DE-188 DE-706 |
| physical | XV, 327 S. graph. Darst. |
| psigel | TUB-nb |
| publishDate | 1975 |
| publishDateSearch | 1975 |
| publishDateSort | 1975 |
| publisher | Springer |
| record_format | marc |
| series | Graduate texts in mathematics. |
| series2 | Graduate texts in mathematics. |
| spelling | Husemöller, Dale Verfasser (DE-588)117713058 aut Fibre bundles Dale Husemöller 2. ed. New York u.a. Springer 1975 XV, 327 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Graduate texts in mathematics. 20. Differentiaalmeetkunde gtt Faisceaux fibrés (Mathématiques) Vezels (wiskunde) gtt Fiber bundles (Mathematics) Faserbündel (DE-588)4135582-9 gnd rswk-swf Algebraische Topologie (DE-588)4120861-4 gnd rswk-swf K-Theorie (DE-588)4033335-8 gnd rswk-swf (DE-588)4151278-9 Einführung gnd-content K-Theorie (DE-588)4033335-8 s DE-604 Faserbündel (DE-588)4135582-9 s Algebraische Topologie (DE-588)4120861-4 s Graduate texts in mathematics. 20. (DE-604)BV000000067 20. HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001280184&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001280184&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Husemöller, Dale Fibre bundles Graduate texts in mathematics. Differentiaalmeetkunde gtt Faisceaux fibrés (Mathématiques) Vezels (wiskunde) gtt Fiber bundles (Mathematics) Faserbündel (DE-588)4135582-9 gnd Algebraische Topologie (DE-588)4120861-4 gnd K-Theorie (DE-588)4033335-8 gnd |
| subject_GND | (DE-588)4135582-9 (DE-588)4120861-4 (DE-588)4033335-8 (DE-588)4151278-9 |
| title | Fibre bundles |
| title_auth | Fibre bundles |
| title_exact_search | Fibre bundles |
| title_full | Fibre bundles Dale Husemöller |
| title_fullStr | Fibre bundles Dale Husemöller |
| title_full_unstemmed | Fibre bundles Dale Husemöller |
| title_short | Fibre bundles |
| title_sort | fibre bundles |
| topic | Differentiaalmeetkunde gtt Faisceaux fibrés (Mathématiques) Vezels (wiskunde) gtt Fiber bundles (Mathematics) Faserbündel (DE-588)4135582-9 gnd Algebraische Topologie (DE-588)4120861-4 gnd K-Theorie (DE-588)4033335-8 gnd |
| topic_facet | Differentiaalmeetkunde Faisceaux fibrés (Mathématiques) Vezels (wiskunde) Fiber bundles (Mathematics) Faserbündel Algebraische Topologie K-Theorie Einführung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001280184&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001280184&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000000067 |
| work_keys_str_mv | AT husemollerdale fibrebundles |
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Inhaltsverzeichnis