Equivariant ordinary homology and cohomology:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
[Cham]
Springer
[2016]
|
| Series: | Lecture Notes in Mathematics
2178 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | xiv, 294 Seiten |
| ISBN: | 9783319504476 |
Staff View
MARC
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| 245 | 1 | 0 | |a Equivariant ordinary homology and cohomology |c Steven R. Costenoble, Stefan Waner |
| 264 | 1 | |a [Cham] |b Springer |c [2016] | |
| 264 | 4 | |c © 2016 | |
| 300 | |a xiv, 294 Seiten | ||
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| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Lecture Notes in Mathematics |v 2178 | |
| 650 | 4 | |a Mathematics | |
| 650 | 4 | |a Category theory (Mathematics) | |
| 650 | 4 | |a Homological algebra | |
| 650 | 4 | |a Topological groups | |
| 650 | 4 | |a Lie groups | |
| 650 | 4 | |a Algebraic topology | |
| 650 | 4 | |a Manifolds (Mathematics) | |
| 650 | 4 | |a Complex manifolds | |
| 650 | 4 | |a Algebraic Topology | |
| 650 | 4 | |a Manifolds and Cell Complexes (incl. Diff.Topology) | |
| 650 | 4 | |a Category Theory, Homological Algebra | |
| 650 | 4 | |a Topological Groups, Lie Groups | |
| 650 | 4 | |a Mathematik | |
| 700 | 1 | |a Waner, Stefan |d 1949- |0 (DE-588)1014760100 |4 aut | |
| 776 | 0 | 8 | |i Erscheint auch als |n Online-Ausgabe |z 978-3-319-50448-3 |
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Record in the Search Index
| _version_ | 1804177036198019072 |
|---|---|
| adam_text | Contents
1 RO (G)-Graded Ordinary Homology and Cohomology.................. 1
1.1 Examples of Equivariant Cell Complexes...................... 3
1.1.1 G-CW Complexes....................................... 3
1.1.2 G-CW(F) Complexes.................................. 6
■1.1.3 Dual G-CW(V) Complexes............................. 8
1.2 Dimension Functions ....................................... 10
1.3 Virtual Representations.................................... 14
1.4 Cell Complexes............. —........................... 15
1.5 A Brief Introduction to Equivariant Stable Homotopy........ 29
1.6 The Algebra of Mackey Functors........................... 32
1.7 Homology and Cohomology of Cell Complexes................. 40
1.8 Ordinary and Dual Homology and Cohomology................ 47
1.9 Stable G~CW Approximation of Spaces........................ 48
1.10 Homology and Cohomology of Spaces.......................... 53
1.10.1 Cellular Chains of G-Spaces......................... 53
1.10.2 Definition and Properties of Homology
and Cohomology.................................... 54
1.10.3 Independence of Choices........................... 64
1.11 Atiyah-Hirzebruch Spectral Sequences and Uniqueness..... 69
1.12 The Representing Spectra................................. 72
1.13 Change of Groups........................................... 77
1.13.1 Subgroups........................................... 77
1.13.2 Quotient Groups................................... 85
1.13.3 Subgroups of Quotient Groups....................... 105
1.14 Products.................................................. 112
1.14.1 Product Complexes.................................. 112
1.14.2 Cup Products....................................... 115
1.14.3 Slant Products, Evaluations, and Cap Products...... 129
1.15 The Thom Isomorphism and Poincaré Duality................. 136
1.15.1 The Thom Isomorphism............................... 136
1.15.2 Poincaré Duality................................... 139
xiii
xiv Contents
1.16 An Example: The Rotating Sphere ........................... 143
1.17 A Survey of Calculations................................... 146
1.18 Relationship to B orel Homology ............................ 150
1.19 Miscellaneous Remarks...................................... 152
1.19.1 Ordinary Homology of G-Spectra...................... 152
1.19.2 Model Categories........................... —*...... 153
2 Parametrized Homotopy Theory and Fundamental Groupoids............. 155
2.1 The Fundamental Groupoid................................... 156
2.2 Parametrized Spaces and Lax Maps........................... 159
2.3 Lax Maps and Model Categories .............................. 164
2.4 Parametrized Spectra........................................ 166
2.5 Lax Maps of Spectra......................................... 169
2.6 The Stable Fundamental Groupoid............................. 178
2.7 Parametrized Homology and Cohomology Theories.............. 187
2.8 Representing Parametrized Homology
and Cohomology Theories..................................... 190
2.9 Duality.................................................... 194
3 RO(IH?)-Graded Ordinary Homology and Cohomology................... 203
3.1 Examples of Parametrized Cell Complexes..................... 204
3.1.1 G-CW(y) Complexes.................................. 204
3.1.2 Dual G-CW(y) Complexes ............................ 206
3.2 S-G-CW(y) Complexes........................................ 207
3.3 Homology and Cohomology of Parametrized Cell Complexes..... 215
3.4 Stable G-CW Approximation of Parametrized Spaces .......... 219
3.5 Homology and Cohomology of Parametrized Spaces ............. 222
3.6 Atiyah-Hirzebruch Spectral Sequences and Uniqueness......... 229
3.7 The Representing Spectra.................................... 230
3.8 Change of Base Space........................................ 233
3.9 Change of Groups.........................................— 241
3.9.1 Subgroups........................................... 241
3.9.2 Quotient Groups.................................... 247
3.9.3 Subgroups of Quotient Groups........................ 256
3.10 Products................................................... 260
3.10.1 Cup Products........................................ 260
3.10.2 Slant Products, Evaluations, and Cap Products....... 269
3.11 The Thom Isomorphism and Poincare Duality................... 276
3.11.1 The Thom Isomorphism............................ 276
3.11.2 Poincare Duality.................................. 277
3.12 A Calculation............................................. 279
Bibliography....................................................... 283
Index of Notations.................................................. 287
Index
291
|
| any_adam_object | 1 |
| author | Costenoble, Steven R. 1961- Waner, Stefan 1949- |
| author_GND | (DE-588)1014760356 (DE-588)1014760100 |
| author_facet | Costenoble, Steven R. 1961- Waner, Stefan 1949- |
| author_role | aut aut |
| author_sort | Costenoble, Steven R. 1961- |
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| classification_rvk | SI 850 |
| ctrlnum | (OCoLC)973044801 (DE-599)BVBBV044032191 |
| dewey-full | 514.2 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 514 - Topology |
| dewey-raw | 514.2 |
| dewey-search | 514.2 |
| dewey-sort | 3514.2 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV044032191 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:41:41Z |
| institution | BVB |
| isbn | 9783319504476 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-029439435 |
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| physical | xiv, 294 Seiten |
| publishDate | 2016 |
| publishDateSearch | 2016 |
| publishDateSort | 2016 |
| publisher | Springer |
| record_format | marc |
| series | Lecture Notes in Mathematics |
| series2 | Lecture Notes in Mathematics |
| spelling | Costenoble, Steven R. 1961- (DE-588)1014760356 aut Equivariant ordinary homology and cohomology Steven R. Costenoble, Stefan Waner [Cham] Springer [2016] © 2016 xiv, 294 Seiten txt rdacontent n rdamedia nc rdacarrier Lecture Notes in Mathematics 2178 Mathematics Category theory (Mathematics) Homological algebra Topological groups Lie groups Algebraic topology Manifolds (Mathematics) Complex manifolds Algebraic Topology Manifolds and Cell Complexes (incl. Diff.Topology) Category Theory, Homological Algebra Topological Groups, Lie Groups Mathematik Waner, Stefan 1949- (DE-588)1014760100 aut Erscheint auch als Online-Ausgabe 978-3-319-50448-3 Lecture Notes in Mathematics 2178 (DE-604)BV000676446 2178 Digitalisierung UB Regensburg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029439435&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Costenoble, Steven R. 1961- Waner, Stefan 1949- Equivariant ordinary homology and cohomology Lecture Notes in Mathematics Mathematics Category theory (Mathematics) Homological algebra Topological groups Lie groups Algebraic topology Manifolds (Mathematics) Complex manifolds Algebraic Topology Manifolds and Cell Complexes (incl. Diff.Topology) Category Theory, Homological Algebra Topological Groups, Lie Groups Mathematik |
| title | Equivariant ordinary homology and cohomology |
| title_auth | Equivariant ordinary homology and cohomology |
| title_exact_search | Equivariant ordinary homology and cohomology |
| title_full | Equivariant ordinary homology and cohomology Steven R. Costenoble, Stefan Waner |
| title_fullStr | Equivariant ordinary homology and cohomology Steven R. Costenoble, Stefan Waner |
| title_full_unstemmed | Equivariant ordinary homology and cohomology Steven R. Costenoble, Stefan Waner |
| title_short | Equivariant ordinary homology and cohomology |
| title_sort | equivariant ordinary homology and cohomology |
| topic | Mathematics Category theory (Mathematics) Homological algebra Topological groups Lie groups Algebraic topology Manifolds (Mathematics) Complex manifolds Algebraic Topology Manifolds and Cell Complexes (incl. Diff.Topology) Category Theory, Homological Algebra Topological Groups, Lie Groups Mathematik |
| topic_facet | Mathematics Category theory (Mathematics) Homological algebra Topological groups Lie groups Algebraic topology Manifolds (Mathematics) Complex manifolds Algebraic Topology Manifolds and Cell Complexes (incl. Diff.Topology) Category Theory, Homological Algebra Topological Groups, Lie Groups Mathematik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029439435&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000676446 |
| work_keys_str_mv | AT costenoblestevenr equivariantordinaryhomologyandcohomology AT wanerstefan equivariantordinaryhomologyandcohomology |