Operads in algebra, topology and physics:
Gespeichert in:
| Beteiligte Personen: | , , |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
Providence, Rhode Island
American Mathematical Society
[2002]
|
| Schriftenreihe: | Mathematical surveys and monographs
Volume 96 |
| Schlagwörter: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009815927&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Beschreibung: | Hier auch später erschienene, unveränderte Nachdrucke |
| Umfang: | x, 349 Seiten Diagramme |
| ISBN: | 0821821342 9780821843628 |
Internformat
MARC
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| 264 | 1 | |a Providence, Rhode Island |b American Mathematical Society |c [2002] | |
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Datensatz im Suchindex
| _version_ | 1819356904386723840 |
|---|---|
| adam_text | Contents
Preface ix
Part I 1
Chapter 1. Introduction and History 3
A prehistory 3
1.1. Lazard s formal group laws 3
1.2. PROPs and PACTs 4
1.3. Non E operads and operads 5
1.4. Theories 7
1.5. Tree operads 8
1.6. ^loo spaces and loop spaces 9
1.7. jE^ spaces and iterated loop spaces 12
1.8. ^ algebras 13
1.9. Partiality and Aoc categories 14
1.10. Loc algebras 17
1.11. Coc algebras 19
1.12. n ary algebras 19
1.13. Operadic bar construction and Koszul duality 20
1.14. Cyclic operads 21
1.15. Moduli spaces and modular operads 22
1.16. Operadic interpretation of closed string field theory 23
1.17. From topological operads to dg operads 26
1.18. Homotopy invariance in algebra and topology 27
1.19. Formality, quantization and Deligne s conjecture 29
1.20. Insertion operads 31
Part II 35
Chapter 1. Operads in a Symmetric Monoidal Category 37
1.1. Symmetric monoidal categories 37
1.2. Operads 40
1.3. Pseudo operads 45
1.4. Operad algebras 46
1.5. The pseudo operad of labeled rooted trees 50
1.6. The Stasheff associahedra 56
1.7. Operads defined in terms of arbitrary finite sets 60
1.8. Operads as monoids 67
1.9. Free operads and free pseudo operads 71
vii
viii CONTENTS
1.10. Collections, A collections and if operads 84
1.11. The GK construction 86
1.12. Triples 88
Chapter 2. Topology Review of Classical Results 93
2.1. Iterated loop spaces 93
2.2. Recognition 94
2.3. The bar construction: theme and variations 96
2.4. Approximation 97
2.5. T spaces 101
2.6. Homology operations 102
2.7. The linear isometries operad and infinite loop spaces 106
2.8. VF construction 109
2.9. Algebraic structures up to strong homotopy 112
Chapter 3. Algebra 121
3.1. The cobar complex of an operad 121
3.2. Quadratic operads 137
3.3. Koszul operads 145
3.4. A complex relating the two conditions for a Koszul operad 149
3.5. Trees with levels 154
3.6. The spectral sequences relating N(P) and C{V) 158
3.7. Coalgebras and coderivations 165
3.8. The homology and cohomology of operad algebras 173
3.9. The pre Lie structure on Coder(T$,(X)) 182
3.10. Application: minimal models and homotopy algebras 186
Chapter 4. Geometry 203
4.1. Configuration spaces operads and modules 203
4.2. Deligne Knudsen Mumford compactification of moduli spaces 212
4.3. Compactification of configuration spaces of points in Kn 218
4.4. Compactification of configurations of points in a manifold 234
Chapter 5. Generalization of Operads 247
5.1. Cyclic operads 247
5.2. Application: cyclic (co)homology 258
5.3. Modular operads 267
5.4. The Feynman transform 279
5.5. Application: graph complexes 290
5.6. Application: moduli spaces of surfaces of arbitrary genera 304
5.7. Application: closed string field theory 312
Epilog 327
Bibliography 329
Glossary of notations 339
Index 345
|
| any_adam_object | 1 |
| author | Markl, Martin 1960- Shnider, Steven 1945- Stasheff, James D. 1936- |
| author_GND | (DE-588)173358861 (DE-588)172689864 (DE-588)1089790864 |
| author_facet | Markl, Martin 1960- Shnider, Steven 1945- Stasheff, James D. 1936- |
| author_role | aut aut aut |
| author_sort | Markl, Martin 1960- |
| author_variant | m m mm s s ss j d s jd jds |
| building | Verbundindex |
| bvnumber | BV014308802 |
| classification_rvk | SK 300 SK 320 |
| ctrlnum | (OCoLC)318373640 (DE-599)BVBBV014308802 |
| dewey-full | 511.3 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 511 - General principles of mathematics |
| dewey-raw | 511.3 |
| dewey-search | 511.3 |
| dewey-sort | 3511.3 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV014308802 |
| illustrated | Not Illustrated |
| indexdate | 2024-12-20T11:03:00Z |
| institution | BVB |
| isbn | 0821821342 9780821843628 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009815927 |
| oclc_num | 318373640 |
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| owner_facet | DE-355 DE-BY-UBR DE-703 DE-19 DE-BY-UBM DE-11 DE-20 DE-384 |
| physical | x, 349 Seiten Diagramme |
| publishDate | 2002 |
| publishDateSearch | 2002 |
| publishDateSort | 2002 |
| publisher | American Mathematical Society |
| record_format | marc |
| series | Mathematical surveys and monographs |
| series2 | Mathematical surveys and monographs |
| spellingShingle | Markl, Martin 1960- Shnider, Steven 1945- Stasheff, James D. 1936- Operads in algebra, topology and physics Mathematical surveys and monographs Categorías (Matemáticas) Operads Operade (DE-588)4638722-5 gnd Topologie (DE-588)4060425-1 gnd Homotopietheorie (DE-588)4128142-1 gnd Mathematische Physik (DE-588)4037952-8 gnd Algebra (DE-588)4001156-2 gnd |
| subject_GND | (DE-588)4638722-5 (DE-588)4060425-1 (DE-588)4128142-1 (DE-588)4037952-8 (DE-588)4001156-2 |
| title | Operads in algebra, topology and physics |
| title_auth | Operads in algebra, topology and physics |
| title_exact_search | Operads in algebra, topology and physics |
| title_full | Operads in algebra, topology and physics Martin Markl ; Steve Shnider ; Jim Stasheff |
| title_fullStr | Operads in algebra, topology and physics Martin Markl ; Steve Shnider ; Jim Stasheff |
| title_full_unstemmed | Operads in algebra, topology and physics Martin Markl ; Steve Shnider ; Jim Stasheff |
| title_short | Operads in algebra, topology and physics |
| title_sort | operads in algebra topology and physics |
| topic | Categorías (Matemáticas) Operads Operade (DE-588)4638722-5 gnd Topologie (DE-588)4060425-1 gnd Homotopietheorie (DE-588)4128142-1 gnd Mathematische Physik (DE-588)4037952-8 gnd Algebra (DE-588)4001156-2 gnd |
| topic_facet | Categorías (Matemáticas) Operads Operade Topologie Homotopietheorie Mathematische Physik Algebra |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009815927&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000018014 |
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