An introduction to intersection homology theory:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Boca Raton u.a.
Chapman & Hall/CRC
2006
|
| Ausgabe: | 2. ed. |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Includes bibliographical references (p. 211-224) and index |
| Beschreibung: | 229 S. 25 cm |
| ISBN: | 1584881844 |
Internformat
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| 100 | 1 | |a Kirwan, Frances |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a An introduction to intersection homology theory |c Frances Kirwan ; Jonathan Woolf |
| 250 | |a 2. ed. | ||
| 264 | 1 | |a Boca Raton u.a. |b Chapman & Hall/CRC |c 2006 | |
| 300 | |a 229 S. |c 25 cm | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 500 | |a Includes bibliographical references (p. 211-224) and index | ||
| 650 | 7 | |a Complexe variabelen |2 gtt | |
| 650 | 4 | |a Homologie d'intersection | |
| 650 | 4 | |a Intersection homology theory | |
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| 689 | 0 | 1 | |a Homologietheorie |0 (DE-588)4141714-8 |D s |
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| 700 | 1 | |a Woolf, Jonathan |e Verfasser |4 aut | |
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Datensatz im Suchindex
| _version_ | 1804135377078845440 |
|---|---|
| adam_text | Titel: An introduction to intersection homology theory
Autor: Kirwan, Frances
Jahr: 2006
Contents
1 Introduction 1
1.1 Poincare duality.......................... 3
1.2 Morse theory for singular spaces................. 4
1.3 de Rham cohomology and L2-cohomology............ 7
1.4 The cohomology of projective varieties ..........................10
2 Review of homology and cohomology 15
2.1 Simplicial homology ..............................................15
2.2 Singular homology..................................................18
2.3 Homology with closed support....................................20
2.4 Conclusion..........................................................22
2.5 Further reading....................................................23
3 Review of sheaf cohomology and derived categories 25
3.1 Sheaves..............................................................25
3.2 Cech cohomology of sheaves......................................29
3.3 Hypercohomology..................................................33
3.4 Functors and exactness............................................34
3.5 Resolutions of sheaves and of complexes..........................38
3.6 Cohomology and hypercohomology via derived functors .... 42
3.7 Derived categories..................................................43
3.8 Right derived functors ............................................46
3.9 Further reading....................................................47
4 The definition of intersection homology 49
4.1 Stratified spaces and pseudomanifolds............................49
4.2 Simplicial intersection homology..................................51
4.3 Singular intersection homology....................................54
4.4 Simple examples of intersection homology........................54
4.5 Normalisations......................................................56
4.6 Relative groups and the Mayer-Vietoris sequence..............57
4.7 The intersection homology of a cone..............................58
4.8 Functoriality of intersection homology............................61
4.9 Homology with local coefficients.................
4.10 Quasi-projective complex varieties................64
4.11 Further reading..........................71
5 Witt spaces and duality 73
5.1 Generalised Poincare duality................... 73
5.2 Witt spaces ............................ 73
5.3 Signatures of Witt spaces.....................78
5.4 The Witt-bordism groups.....................7^
5.5 Further reading..........................83
6 L2-cohomoIogy and intersection cohomology 85
6.1 L2-cohomology and Hodge theory................85
6.2 The L2-cohomology of a punctured cone ............88
6.3 Varieties with isolated conical singularities...........93
6.4 Locally symmetric varieties....................96
6.5 Further reading..........................191
7 Sheaf-theoretic intersection homology 103
7.1 Sheaves of singular chains.....................103
7.2 Constructibility and an axiomatic characterisation.......107
7.3 The topological invariance of intersection homology......110
7.4 Duality in the derived category..................113
7.5 Further reading..........................116
8 Perverse sheaves 117
8.1 Perverse sheaves..........................117
8.2 Perverse sheaves on varieties...................121
8.3 Nearby and vanishing cycles...................122
8.4 The decomposition theorem ...................125
8.5 Further reading..........................130
9 The intersection cohomology of fans 133
9.1 Affine toric varieties........................133
9.2 Toric varieties from fans .....................137
9.3 Maps and torus actions......................138
9.4 Projective toric varieties and convex polytopes.........140
9.5 Stratifications of toric varieties..................143
9.6 Subdivisions and desingularisations...............144
9.7 Equivariant intersection cohomology...............146
9.8 The intersection cohomology of fans...............150
9.9 Stanley s conjectures .......................158
9.10 Further reading..........................161
10 Characteristic p and the Weil conjectures 163
10.1 Statement of the Weil conjectures................163
10.2 Basic properties of £-adic cohomology..............166
10.3 Etale topology and cohomology.................168
10.4 The Weil conjectures for singular varieties ...........171
10.5 Further reading..........................173
11 TP-Modules and the Riemann-Hilbert correspondence 175
11.1 The Riemann-Hilbert problem..................175
11.2 Differential systems over C71...................178
11.3 TPx-niodules and intersection homology.............180
11.4 The characteristic variety of a TP*-module...........182
11.5 Holonomic differential systems..................185
11.6 Examples of characteristic varieties...............186
11.7 Left and right t x-modules....................189
11.8 Restriction of £ x-modules....................190
11.9 Regular singularities........................193
11.10 The Riemann-Hilbert correspondence..............195
11.11 Further reading..........................197
12 The Kazhdan-Lusztig conjecture 199
12.1 Verma modules ..........................199
12.2 TP-modules over flag manifolds..................203
12.3 Characteristic p..........................206
12.4 Hecke algebras and the Kazhdan-Lusztig polynomials.....207
12.5 Further reading..........................209
Bibliography 211
Index 225
|
| adam_txt |
Titel: An introduction to intersection homology theory
Autor: Kirwan, Frances
Jahr: 2006
Contents
1 Introduction 1
1.1 Poincare duality. 3
1.2 Morse theory for singular spaces. 4
1.3 de Rham cohomology and L2-cohomology. 7
1.4 The cohomology of projective varieties .10
2 Review of homology and cohomology 15
2.1 Simplicial homology .15
2.2 Singular homology.18
2.3 Homology with closed support.20
2.4 Conclusion.22
2.5 Further reading.23
3 Review of sheaf cohomology and derived categories 25
3.1 Sheaves.25
3.2 Cech cohomology of sheaves.29
3.3 Hypercohomology.33
3.4 Functors and exactness.34
3.5 Resolutions of sheaves and of complexes.38
3.6 Cohomology and hypercohomology via derived functors . 42
3.7 Derived categories.43
3.8 Right derived functors .46
3.9 Further reading.47
4 The definition of intersection homology 49
4.1 Stratified spaces and pseudomanifolds.49
4.2 Simplicial intersection homology.51
4.3 Singular intersection homology.54
4.4 Simple examples of intersection homology.54
4.5 Normalisations.56
4.6 Relative groups and the Mayer-Vietoris sequence.57
4.7 The intersection homology of a cone.58
4.8 Functoriality of intersection homology.61
4.9 Homology with local coefficients.
4.10 Quasi-projective complex varieties.64
4.11 Further reading.71
5 Witt spaces and duality 73
5.1 Generalised Poincare duality. 73
5.2 Witt spaces . 73
5.3 Signatures of Witt spaces.78
5.4 The Witt-bordism groups.7^
5.5 Further reading.83
6 L2-cohomoIogy and intersection cohomology 85
6.1 L2-cohomology and Hodge theory.85
6.2 The L2-cohomology of a punctured cone .88
6.3 Varieties with isolated conical singularities.93
6.4 Locally symmetric varieties.96
6.5 Further reading.191
7 Sheaf-theoretic intersection homology 103
7.1 Sheaves of singular chains.103
7.2 Constructibility and an axiomatic characterisation.107
7.3 The topological invariance of intersection homology.110
7.4 Duality in the derived category.113
7.5 Further reading.116
8 Perverse sheaves 117
8.1 Perverse sheaves.117
8.2 Perverse sheaves on varieties.121
8.3 Nearby and vanishing cycles.122
8.4 The decomposition theorem .125
8.5 Further reading.130
9 The intersection cohomology of fans 133
9.1 Affine toric varieties.133
9.2 Toric varieties from fans .137
9.3 Maps and torus actions.138
9.4 Projective toric varieties and convex polytopes.140
9.5 Stratifications of toric varieties.143
9.6 Subdivisions and desingularisations.144
9.7 Equivariant intersection cohomology.146
9.8 The intersection cohomology of fans.150
9.9 Stanley's conjectures .158
9.10 Further reading.161
10 Characteristic p and the Weil conjectures 163
10.1 Statement of the Weil conjectures.163
10.2 Basic properties of £-adic cohomology.166
10.3 Etale topology and cohomology.168
10.4 The Weil conjectures for singular varieties .171
10.5 Further reading.173
11 TP-Modules and the Riemann-Hilbert correspondence 175
11.1 The Riemann-Hilbert problem.175
11.2 Differential systems over C71.178
11.3 TPx-niodules and intersection homology.180
11.4 The characteristic variety of a TP*-module.182
11.5 Holonomic differential systems.185
11.6 Examples of characteristic varieties.186
11.7 Left and right t x-modules.189
11.8 Restriction of £ x-modules.190
11.9 Regular singularities.193
11.10 The Riemann-Hilbert correspondence.195
11.11 Further reading.197
12 The Kazhdan-Lusztig conjecture 199
12.1 Verma modules .199
12.2 TP-modules over flag manifolds.203
12.3 Characteristic p.206
12.4 Hecke algebras and the Kazhdan-Lusztig polynomials.207
12.5 Further reading.209
Bibliography 211
Index 225 |
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| isbn | 1584881844 |
| language | English |
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| spelling | Kirwan, Frances Verfasser aut An introduction to intersection homology theory Frances Kirwan ; Jonathan Woolf 2. ed. Boca Raton u.a. Chapman & Hall/CRC 2006 229 S. 25 cm txt rdacontent n rdamedia nc rdacarrier Includes bibliographical references (p. 211-224) and index Complexe variabelen gtt Homologie d'intersection Intersection homology theory Homologietheorie (DE-588)4141714-8 gnd rswk-swf Schnitttheorie (DE-588)4179890-9 gnd rswk-swf Schnitttheorie (DE-588)4179890-9 s Homologietheorie (DE-588)4141714-8 s DE-604 Woolf, Jonathan Verfasser aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014812509&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Kirwan, Frances Woolf, Jonathan An introduction to intersection homology theory Complexe variabelen gtt Homologie d'intersection Intersection homology theory Homologietheorie (DE-588)4141714-8 gnd Schnitttheorie (DE-588)4179890-9 gnd |
| subject_GND | (DE-588)4141714-8 (DE-588)4179890-9 |
| title | An introduction to intersection homology theory |
| title_auth | An introduction to intersection homology theory |
| title_exact_search | An introduction to intersection homology theory |
| title_exact_search_txtP | An introduction to intersection homology theory |
| title_full | An introduction to intersection homology theory Frances Kirwan ; Jonathan Woolf |
| title_fullStr | An introduction to intersection homology theory Frances Kirwan ; Jonathan Woolf |
| title_full_unstemmed | An introduction to intersection homology theory Frances Kirwan ; Jonathan Woolf |
| title_short | An introduction to intersection homology theory |
| title_sort | an introduction to intersection homology theory |
| topic | Complexe variabelen gtt Homologie d'intersection Intersection homology theory Homologietheorie (DE-588)4141714-8 gnd Schnitttheorie (DE-588)4179890-9 gnd |
| topic_facet | Complexe variabelen Homologie d'intersection Intersection homology theory Homologietheorie Schnitttheorie |
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