Rational homotopy theory and differential forms:
Gespeichert in:
| Beteiligte Personen: | , |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
New York, NY [u.a.]
Birkhäuser
2013
|
| Ausgabe: | 2. ed. |
| Schriftenreihe: | Progress in mathematics
16 |
| Schlagwörter: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026820180&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Umfang: | XI, 224 S. graph. Darst. |
| ISBN: | 1461484677 9781461484677 (eBook) 9781461484684 |
Internformat
MARC
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| 245 | 1 | 0 | |a Rational homotopy theory and differential forms |c Phillip A. Griffiths ; John Morgan |
| 250 | |a 2. ed. | ||
| 264 | 1 | |a New York, NY [u.a.] |b Birkhäuser |c 2013 | |
| 300 | |a XI, 224 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Progress in mathematics |v 16 | |
| 650 | 7 | |a Differentiaalvormen |2 gtt | |
| 650 | 4 | |a Formes différentielles | |
| 650 | 4 | |a Homotopie | |
| 650 | 7 | |a Homotopie |2 gtt | |
| 650 | 4 | |a Differential forms | |
| 650 | 4 | |a Homotopy theory | |
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Datensatz im Suchindex
| _version_ | 1819250583514644480 |
|---|---|
| adam_text | Contents
1 Introduction....................................................... 1
2 Basic Concepts..................................................... 5
2.1 CW Complexes.............................................. 5
2.2 First Notions from Homotopy Theory.......................... 8
2.3 Homology .................................................. 13
2.4 Categories and Functors ................................... 19
3 CW Homology Theorem............................................... 21
3.1 The Statement.............................................. 21
3.2 The Proof.................................................. 22
3.3 Examples .................................................. 24
4 The Whitehead Theorem and the Hurewicz Theorem.................... 27
4.1 Definitions and Elementary Properties
of Homotopy Groups..................................... — 27
4.2 The Whitehead Theorem...................................... 29
4.3 Completion of the Computation of 7tn(Sn)................... 31
4.4 The Hurewicz Theorem..................................... 33
4.5 Corollaries of the Hurewicz Theorem........................ 34
4.6 Homotopy Theory of a Fibration............................. 38
4.7 Applications of the Exact Homotopy Sequence................ 39
5 Spectral Sequence of a Fibration.................................. 41
5.1 Introduction............................................... 41
5.2 Fibrations over a Cell..................................... 42
5.3 Generalities on Spectral Sequences......................... 43
5.4 The Leray—Serre Spectral Sequence of a Fibration........... 45
5.5 Examples................................................... 48
6 Obstruction Theory................................................ 53
6.1 Introduction............................................... 53
6.2 Definition and Properties of the Obstruction Cocycle....... 54
IX
Contents
6.3 Further Properties.......................................... 57
6.4 Obstruction to the Existence of a Section of a Fibration.... 58
6.5 Examples..................................................... 58
Eilenberg-MacLane Spaces, Cohomology, and Principal Fibrations. 63
7.1 Relation of Cohomology and Eilenberg-MacLane Spaces ........ 63
7.2 Principal K(ti, n)-Fibrations..............»................. 64
Postnikov Towers and Rational Homotopy Theory................... 69
8.1 Rational Homotopy Theory for Simply Connected Spaces ....... 73
8.2 Construction of the Localization of a Space................ 79
deRham’s Theorem for Simplicial Complexes.......................... 83
9.1 Piecewise Linear Forms.................................... 83
9.2 Lemmas About Piecewise Linear Forms....................... 85
9.3 Naturality Under Subdivision................................ 88
9.4 Multiplicativity of the deRham Isomorphism.................. 89
9.5 Connection with the C°° deRham Theorem...................... 90
9.6 Generalizations of the Construction......................... 92
Differential Graded Algebras....................................... 95
10.1 Introduction.............................................. 95
10.2 Hirsch Extensions.......................................... 97
10.3 Relative Cohomology......................................... 99
10.4 Construction of the Minimal Model......................... 100
Homotopy Theory of DGAs........................................... 103
11.1 Homotopies................................................. 103
11.2 Obstruction Theory........................................... 104
11.3 Applications of Obstruction Theory......................... 107
11.4 Uniqueness of the Minimal Model............................ 109
DGAs and Rational Homotopy Theory................................ 113
12.1 Transgression in the Serre Spectral Sequence and the Duality. 113
12.2 Hirsch Extensions and Principal Fibrations................. 114
12.3 Minimal Models and Postnikov Towers..................... 115
12.4 The Minimal Model of the deRham Complex.................... 117
The Fundamental Group............................................ 119
13.1 1-Minimal Models .......................................... 119
13.2 Tti 0 Q.................................................... 120
13.3 Functorality............................................... 123
13.4 Examples................................................... 125
Examples and Computations......................................... 127
14.1 Spheres and Projective Spaces.............................. 127
14.2 Graded Lie Algebras........................................ 12g
14.3 The Borromean Rings........................................ 129
14.4 Symmetric Spaces and Formality............................. 131
Contents xi
14.5 The Third Homotopy Group of a Simply Connected Space....... 132
14.6 Homotopy Theory of Certain 4-Dimensional Complexes.......... 134
14.7 Q-Homotopy Type of BUn and Un............................... 135
14.8 Products.................................................... 137
14.9 Massey Products............................................. 138
15 Functorality....................................................... 141
15.1 The Functorial Correspondence.............................. 141
15.2 Bijectivity of Homotopy Classes of Maps..................... 144
15.3 Equivalence of Categories................................... 148
16 The Hirsch Lemma................................................... 151
16.1 The Cubical Complex and Cubical Forms..................... 151
16.2 Hirsch Extensions and Spectral Sequences.................... 154
16.3 Polynomial Forms for a Serre Fibration...................... 156
16.4 Serre Spectral Sequence for Polynomial Forms................ 159
16.5 Proof of Theorem 12.1....................................... 163
17 Quillen’s Work on Rational Homotopy Theory......................... 165
17.1 Differential Graded Lie Algebras............................ 165
17.2 Differential Graded Co-algebras............................. 166
17.3 The Bar Construction........................................ 167
17.4 Relationship Between Quillen’s Construction and Sullivan’s. 169
17.5 Quillen’s Construction...................................... 169
18 A oo-Structures and Coo-Structures................................. 177
18.1 Operads, Rooted Trees, and Stasheff’s Associahedron.......... 177
18.2 Aoo՜Algebras and Aoq-Categories............................. 181
18.3 Coo - Algebras and DG As..................................... 183
19 Exercises.......................................................... 187
References.............................................................. 223
|
| any_adam_object | 1 |
| author | Griffiths, Phillip 1938- Morgan, John W. 1946- |
| author_GND | (DE-588)131881434 (DE-588)129352446 |
| author_facet | Griffiths, Phillip 1938- Morgan, John W. 1946- |
| author_role | aut aut |
| author_sort | Griffiths, Phillip 1938- |
| author_variant | p g pg j w m jw jwm |
| building | Verbundindex |
| bvnumber | BV041372040 |
| callnumber-first | Q - Science |
| callnumber-label | QA612 |
| callnumber-raw | QA612.7 |
| callnumber-search | QA612.7 |
| callnumber-sort | QA 3612.7 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 300 |
| ctrlnum | (OCoLC)861677705 (DE-599)BVBBV041372040 |
| dewey-full | 514/.24 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 514 - Topology |
| dewey-raw | 514/.24 |
| dewey-search | 514/.24 |
| dewey-sort | 3514 224 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 2. ed. |
| format | Book |
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| id | DE-604.BV041372040 |
| illustrated | Illustrated |
| indexdate | 2024-12-20T16:45:57Z |
| institution | BVB |
| isbn | 1461484677 9781461484677 (eBook) 9781461484684 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-026820180 |
| oclc_num | 861677705 |
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| owner_facet | DE-19 DE-BY-UBM DE-11 DE-83 DE-355 DE-BY-UBR DE-188 |
| physical | XI, 224 S. graph. Darst. |
| publishDate | 2013 |
| publishDateSearch | 2013 |
| publishDateSort | 2013 |
| publisher | Birkhäuser |
| record_format | marc |
| series | Progress in mathematics |
| series2 | Progress in mathematics |
| spellingShingle | Griffiths, Phillip 1938- Morgan, John W. 1946- Rational homotopy theory and differential forms Progress in mathematics Differentiaalvormen gtt Formes différentielles Homotopie Homotopie gtt Differential forms Homotopy theory Homotopietheorie (DE-588)4128142-1 gnd Homotopie (DE-588)4025803-8 gnd Differentialform (DE-588)4149772-7 gnd |
| subject_GND | (DE-588)4128142-1 (DE-588)4025803-8 (DE-588)4149772-7 |
| title | Rational homotopy theory and differential forms |
| title_auth | Rational homotopy theory and differential forms |
| title_exact_search | Rational homotopy theory and differential forms |
| title_full | Rational homotopy theory and differential forms Phillip A. Griffiths ; John Morgan |
| title_fullStr | Rational homotopy theory and differential forms Phillip A. Griffiths ; John Morgan |
| title_full_unstemmed | Rational homotopy theory and differential forms Phillip A. Griffiths ; John Morgan |
| title_short | Rational homotopy theory and differential forms |
| title_sort | rational homotopy theory and differential forms |
| topic | Differentiaalvormen gtt Formes différentielles Homotopie Homotopie gtt Differential forms Homotopy theory Homotopietheorie (DE-588)4128142-1 gnd Homotopie (DE-588)4025803-8 gnd Differentialform (DE-588)4149772-7 gnd |
| topic_facet | Differentiaalvormen Formes différentielles Homotopie Differential forms Homotopy theory Homotopietheorie Differentialform |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026820180&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000004120 |
| work_keys_str_mv | AT griffithsphillip rationalhomotopytheoryanddifferentialforms AT morganjohnw rationalhomotopytheoryanddifferentialforms |