The theory of transformation groups
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| 1. Verfasser: | |
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| Format: | Buch |
| Sprache: | English Japanese |
| Veröffentlicht: |
Oxford [u.a.]
Oxford Univ. Press
1991
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| Online-Zugang: | Inhaltsverzeichnis |
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| 100 | 1 | |a Kawakubo, Katsuo |e Verfasser |4 aut | |
| 240 | 1 | 0 | |a Henkan gunron |
| 245 | 1 | 0 | |a The theory of transformation groups |c Katsuo Kawakubo |
| 264 | 1 | |a Oxford [u.a.] |b Oxford Univ. Press |c 1991 | |
| 300 | |a X, 338 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 500 | |a Aus dem Japan. übers. | ||
| 650 | 4 | |a Transformations, Groupes de | |
| 650 | 7 | |a Transformations, groupes de |2 ram | |
| 650 | 4 | |a Transformation groups | |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-002977978 | ||
Datensatz im Suchindex
| _version_ | 1804118950096666624 |
|---|---|
| adam_text | Contents
1. Topological transformation groups l
1.1 Definitions and fundamental properties of
transformation groups 1
1.2 Topological groups 7
1.3 Examples of topological groups and semi direct products 14
1.4 Topological transformation groups 23
1.5 Fixed point sets 31
1.6 Orbits and orbit spaces 35
1.7 Homogeneous spaces and equivariant maps
between them 41
1.8 Orbit types and isotropy types 49
1.9 Induced transformation groups 52
Exercises 62
2. Fibre bundles 64
2.1 Fibre bundles 64
2.2 G1 G2 bispaces and twisted products 68
2.3 Principal bundles and associated bundles 73
2.4 Fibre products and induced bundles 78
2.5 G vector bundles 82
2.6 The classification of G vector bundles over G/H 89
2.7 Invariant integration on a compact topological group 94
2.8 G invariant metrics on G vector bundles and orthogonal
complements 100
Exercises 104
3. Manifolds and Lie groups 105
3.1 Manifolds and examples 105
3.2 Lie groups and their actions 112
3.3 Tangent spaces 116
3.4 Tangent G vector bundles 124
3.5 Vector fields and 1 parameter groups 129
3.6 Left invariant vector fields on Lie groups and the
exponential map 136
3.7 A closed subgroup of a Lie group is a Lie subgroup 148
3.8 Differential structures on homogeneous spaces G/H and
local cross sections 152
x I Contents
3.9 Semi direct products of Lie groups and examples of
homogeneous spaces 160
Exercises 168
4. Structure of G manifolds 169
4.1 G embeddings and orbits 169
4.2 Geodesies and the exponential map 173
4.3 G invariant tubular neighbourhoods 177
4.4 The slice theorem 186
4.5 Structure theorems for G manifolds 192
4.6 Decomposition and blowing up of G manifolds 203
4.7 Finiteness of number of orbit types 212
4.8 Principal orbits 215
4.9 Dimension of compact Lie groups which act effectively
on manifolds 221
Exercises 224
5. Algebraization 226
5.1 G complexes 226
5.2 Formulae for Euler characteristics and Mobius inversion 234
5.3 The transfer 246
5.4 Zp actions and the Smith homology group 251
5.5 The Smith theory 254
5.6 Applications to G manifolds 257
5.7 The Lefschetz fixed point theorem 265
5.8 Free and semi free transformation groups on spheres 270
Exercises 277
6. Localization and Riemann Roch type
theorems 278
6.1 Equivariant Gysin homomorphism 278
6.2 Localization theorems 285
6.3 The G signature theorem 296
6.4 Equivariant Riemann Roch theorems 303
6.5 The vanishing theorem of the i genus 309
6.6 Vanishing theorems of exp(c/2) A genera 311
Exercises 320
Answers to Exercises 321
Bibliography 327
Index 335
|
| any_adam_object | 1 |
| author | Kawakubo, Katsuo |
| author_facet | Kawakubo, Katsuo |
| author_role | aut |
| author_sort | Kawakubo, Katsuo |
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| bvnumber | BV004836887 |
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| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 260 SK 350 |
| ctrlnum | (OCoLC)23287145 (DE-599)BVBBV004836887 |
| dewey-full | 512/.72 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512/.72 |
| dewey-search | 512/.72 |
| dewey-sort | 3512 272 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV004836887 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T16:18:26Z |
| institution | BVB |
| isbn | 0198532121 |
| language | English Japanese |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-002977978 |
| oclc_num | 23287145 |
| open_access_boolean | |
| owner | DE-12 DE-384 DE-739 DE-824 DE-19 DE-BY-UBM DE-20 DE-83 DE-11 DE-188 |
| owner_facet | DE-12 DE-384 DE-739 DE-824 DE-19 DE-BY-UBM DE-20 DE-83 DE-11 DE-188 |
| physical | X, 338 S. graph. Darst. |
| publishDate | 1991 |
| publishDateSearch | 1991 |
| publishDateSort | 1991 |
| publisher | Oxford Univ. Press |
| record_format | marc |
| spelling | Kawakubo, Katsuo Verfasser aut Henkan gunron The theory of transformation groups Katsuo Kawakubo Oxford [u.a.] Oxford Univ. Press 1991 X, 338 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Aus dem Japan. übers. Transformations, Groupes de Transformations, groupes de ram Transformation groups Transformationsgruppe (DE-588)4127386-2 gnd rswk-swf Transformationsgruppe (DE-588)4127386-2 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002977978&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Kawakubo, Katsuo The theory of transformation groups Transformations, Groupes de Transformations, groupes de ram Transformation groups Transformationsgruppe (DE-588)4127386-2 gnd |
| subject_GND | (DE-588)4127386-2 |
| title | The theory of transformation groups |
| title_alt | Henkan gunron |
| title_auth | The theory of transformation groups |
| title_exact_search | The theory of transformation groups |
| title_full | The theory of transformation groups Katsuo Kawakubo |
| title_fullStr | The theory of transformation groups Katsuo Kawakubo |
| title_full_unstemmed | The theory of transformation groups Katsuo Kawakubo |
| title_short | The theory of transformation groups |
| title_sort | the theory of transformation groups |
| topic | Transformations, Groupes de Transformations, groupes de ram Transformation groups Transformationsgruppe (DE-588)4127386-2 gnd |
| topic_facet | Transformations, Groupes de Transformations, groupes de Transformation groups Transformationsgruppe |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002977978&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT kawakubokatsuo henkangunron AT kawakubokatsuo thetheoryoftransformationgroups |