Rational homotopy type: a constructive study via the theory of the I*-measure
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin ; Heidelberg ; New York ; London ; Paris ; Tokyo
Springer
1987
|
| Schriftenreihe: | Lecture notes in mathematics
1264 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | VIII, 219 Seiten |
| ISBN: | 3540136118 0387136118 |
Internformat
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| 100 | 1 | |a Wu, Wenjun |d 1919-2017 |0 (DE-588)111549116 |4 aut | |
| 245 | 1 | 0 | |a Rational homotopy type |b a constructive study via the theory of the I*-measure |c Wu Wen-tsün |
| 264 | 1 | |a Berlin ; Heidelberg ; New York ; London ; Paris ; Tokyo |b Springer |c 1987 | |
| 300 | |a VIII, 219 Seiten | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Lecture notes in mathematics |v 1264 | |
| 650 | 4 | |a Differential algebra | |
| 650 | 4 | |a Homotopy theory | |
| 650 | 4 | |a Measure theory | |
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Datensatz im Suchindex
| _version_ | 1805071482814988288 |
|---|---|
| adam_text |
CONTENTS
Preface III
Chapter I Fundamental Concepts — Measure and Calculability . 1
1. The Notion of Measure 1
2. Examples in Measures with Applications 4
3. Adequacy of Measures 12
4. Geometrical Category of Homotopic -Simplicial Spaces 18
Chapter II DGA and Minimal Model 20
1. Notion of DGA and its Homology 20
2. DGA-Morphisms and Homotopy of DGA's 24
3. Minimal Model of a DGA-Existence 29
4. Minimal Model of a DGA—Uniqueness 34
5. Induced Morphisms of Minimal DGA's . 41
6. Some Auxiliary Theorems about Twisted Products 50
*
Chapter III The DeRham -Sullivan Theorem and I -Measure 58
1. The DeRham -Sullivan Algebra of a Simplicial Complex and the deRham-
Sullivan Theorem 58
2. The Weil DGA of a Complex 60
3. Proof of the deRham-Sullivan Theorem 66
4. Integration and Duality 78
5. Homotopy Invariance and Calculability of I -Measure 87
Chapter IV I -Measure and Homotopy 93
1. The Cartan -Serre Extension of a DGA and the Hurewicz Number . 93
2. The Cartan -Serre Extension of a Space 96
3. The Cartan -Serre Tower of a Space and the Hurewicz Homomorphism . . 101
4. Whitehead Products of Homotopy Groups 106
Chapter V I -Measure of a Homogeneous Space - The Cartan Theorem 116
1. DGA of Left-Invariant Forms on a Lie Group 116
2. Homogeneous Space and Invariant Forms — Method of E. Cartan . 123
3. The Weil Algebra 127
4. The Cartan Algebra and the Theorem of Cartan 135
Chapter VI Effective Computation and Axiomatic System of I -Measure . 143
1. An Extension Theorem . . 143
2. Union of Complexes along a Subcomplex 148
3. Some Particular Cases - Cone-Construction and Suspension 155
4. Effective Computation and Axiomatic System of I*-Measure * 161
5. Some Applications to Fibrations - Fiber Space Theorem 165
6. Some Applications to Fibrations - Transgression and a Theorem of Bo-
rel-Hirsch 173
Chapter VII I -Measures Connected with 'Fibrations 178
1. Some Algebraic Preparations 178
2. Simplicial Fibration and some Spectral Sequences 184
3. Fiber-Square Constructions and Fiber-Square Theorem for I -Measures 191
4. Proof of the Fiber-Square Theorem 197
5. Fiber-Space Theorem and other Applications 202
Bibliography 214
Index 218 |
| any_adam_object | 1 |
| author | Wu, Wenjun 1919-2017 |
| author_GND | (DE-588)111549116 |
| author_facet | Wu, Wenjun 1919-2017 |
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| dewey-full | 510 |
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| dewey-ones | 510 - Mathematics |
| dewey-raw | 510 |
| dewey-search | 510 |
| dewey-sort | 3510 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV000737032 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-20T04:38:31Z |
| institution | BVB |
| isbn | 3540136118 0387136118 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-000461387 |
| oclc_num | 230893090 |
| open_access_boolean | |
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| physical | VIII, 219 Seiten |
| publishDate | 1987 |
| publishDateSearch | 1987 |
| publishDateSort | 1987 |
| publisher | Springer |
| record_format | marc |
| series | Lecture notes in mathematics |
| series2 | Lecture notes in mathematics |
| spelling | Wu, Wenjun 1919-2017 (DE-588)111549116 aut Rational homotopy type a constructive study via the theory of the I*-measure Wu Wen-tsün Berlin ; Heidelberg ; New York ; London ; Paris ; Tokyo Springer 1987 VIII, 219 Seiten txt rdacontent n rdamedia nc rdacarrier Lecture notes in mathematics 1264 Differential algebra Homotopy theory Measure theory Differentialform (DE-588)4149772-7 gnd rswk-swf Homotopie (DE-588)4025803-8 gnd rswk-swf Graduierte Algebra (DE-588)4304029-9 gnd rswk-swf Differentialalgebra (DE-588)4134657-9 gnd rswk-swf Homotopie (DE-588)4025803-8 s Differentialform (DE-588)4149772-7 s Graduierte Algebra (DE-588)4304029-9 s 1\p DE-604 Differentialalgebra (DE-588)4134657-9 s 2\p DE-604 Lecture notes in mathematics 1264 (DE-604)BV000676446 1264 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000461387&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Wu, Wenjun 1919-2017 Rational homotopy type a constructive study via the theory of the I*-measure Lecture notes in mathematics Differential algebra Homotopy theory Measure theory Differentialform (DE-588)4149772-7 gnd Homotopie (DE-588)4025803-8 gnd Graduierte Algebra (DE-588)4304029-9 gnd Differentialalgebra (DE-588)4134657-9 gnd |
| subject_GND | (DE-588)4149772-7 (DE-588)4025803-8 (DE-588)4304029-9 (DE-588)4134657-9 |
| title | Rational homotopy type a constructive study via the theory of the I*-measure |
| title_auth | Rational homotopy type a constructive study via the theory of the I*-measure |
| title_exact_search | Rational homotopy type a constructive study via the theory of the I*-measure |
| title_full | Rational homotopy type a constructive study via the theory of the I*-measure Wu Wen-tsün |
| title_fullStr | Rational homotopy type a constructive study via the theory of the I*-measure Wu Wen-tsün |
| title_full_unstemmed | Rational homotopy type a constructive study via the theory of the I*-measure Wu Wen-tsün |
| title_short | Rational homotopy type |
| title_sort | rational homotopy type a constructive study via the theory of the i measure |
| title_sub | a constructive study via the theory of the I*-measure |
| topic | Differential algebra Homotopy theory Measure theory Differentialform (DE-588)4149772-7 gnd Homotopie (DE-588)4025803-8 gnd Graduierte Algebra (DE-588)4304029-9 gnd Differentialalgebra (DE-588)4134657-9 gnd |
| topic_facet | Differential algebra Homotopy theory Measure theory Differentialform Homotopie Graduierte Algebra Differentialalgebra |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000461387&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000676446 |
| work_keys_str_mv | AT wuwenjun rationalhomotopytypeaconstructivestudyviathetheoryoftheimeasure |