Simplicial and operad methods in algebraic topology:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English Russian |
| Published: |
Providence, RI
AMS
2001
|
| Series: | Translations of mathematical monographs
198 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Aus d. Russ. übers. |
| Physical Description: | X, 235 S. |
| ISBN: | 0821821709 |
Staff View
MARC
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| 100 | 1 | |a Smirnov, Vladimir A. |d 1951- |e Verfasser |0 (DE-588)10336627X |4 aut | |
| 240 | 1 | 0 | |a Simplicialʹnye i operadnye metody v algebraičeskoj topologii |
| 245 | 1 | 0 | |a Simplicial and operad methods in algebraic topology |c V. A. Smirnov |
| 264 | 1 | |a Providence, RI |b AMS |c 2001 | |
| 300 | |a X, 235 S. | ||
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| 500 | |a Aus d. Russ. übers. | ||
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| 650 | 4 | |a Topologie algébrique | |
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| 650 | 4 | |a Algebraic topology | |
| 650 | 4 | |a Operads | |
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Record in the Search Index
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|---|---|
| adam_text | Contents
Preface ix
Chapter 1. Operads in the Category of Topological Spaces 1
1.1. ^loc structure on a loop space 1
1.2. Operads and spaces over operads 3
1.3. Little cubes operads and loop spaces 7
1.4. Operads and monads 10
1.5. Bioperads in the category of topological spaces 13
Chapter 2. Simplicial Objects and Homotopy Theory 19
2.1. Simplicial and cosimplicial objects 19
2.2. Simplicial sets 25
2.3. Ax simplicial objects and yloo topological groups 30
2.4. Homotopy type and ^^ group structure 37
Chapter 3. Algebraic Structures on Chain Complexes 45
3.1. Chain complexes 45
3.2. Algebras and modules over an algebra 49
3.3. Twisted tensor products and functor V 54
3.4. Bar constructions and cobar constructions 66
3.5. Lie modules and comodules 67
3.6. V algebras and A coalgebras 69
Chapter 4. ^oo Structures on Chain Complexes 75
4.1. ^loo algebras and ^loc coalgebras 75
4.2. yloo modules and ^.sc comodules 79
4.3. ^loo V algebras and ^oc A coalgebras 81
4.4. Commutative ^^ algebras and ^oo coalgebras 83
4.5. The functor V for /^ algebras 85
Chapter 5. Operads and Algebras over Operads 89
5.1. Operads in the category of chain complexes 89
5.2. Algebras and coalgebras over operads 95
5.3. Ex structure on cobar constructions 101
5.4. Bar constructions on operads 102
5.5. Bar constructions on algebras over operads 106
5.6. Homology and cohomology of an K^ operad. 109
Chapter 6. Homology of Iterated Loop Spaces 119
6.1. Chain complex of an iterated loop space 119
vii
viii CONTENTS
6.2. Computation of the second term of the spectral sequence of iterated
loop spaces 123
6.3. Homology of iterated loop spaces of real projective spaces 125
6.4. Homology of iterated loop spaces of complex projective spaces 128
Chapter 7. Homotopy Theories and Ex Structures 133
7.1. Localization of categories and homotopy theory 133
7.2. Curtis spectral sequence 135
7.3. Bousfield Kan spectral sequence 139
7.4. Homotopy groups of symmetric products 147
7.5. Homotopy theory of simplicial coalgebras 150
7.6. Homotopy theory of .E^ coalgebras 152
Chapter 8. Operad Methods in Cobordism Theory 157
8.1. Bioperads and classical groups 157
8.2. .E^ multiplicative spectra and Thom spectra 164
8.3. Generalized homology theories and the Dyer Lashof algebra 168
8.4. Generalized cohomology theories and the Steenrod algebra 176
Chapter 9. Description of the Cohomology of Groups and Algebras 183
9.1. Description of Ax algebvas and /l^ modules 183
9.2. Description of the cohomology of groups 187
9.3. Description of the cohomology of Banach algebras 191
9.4. Description of the i?2 term of the Adams spectral sequence for
stable homotopy groups of topological spaces 201
9.5. Description of the .E^ term of the Adams spectral sequence for
unstable homotopy groups of topological spaces 203
Chapter 10. Homology Operations and Differentials in the Adams Spectral
Sequence 209
10.1. Functional homology operations 209
10.2. ^l^ cosimplicial objects 216
10.3. Functorial homology operations 219
10.4. Differentials in the Adams spectral sequence 224
10.5. Description of the homotopy groups of topological spaces 226
Bibliography 231
Index 233
|
| any_adam_object | 1 |
| author | Smirnov, Vladimir A. 1951- |
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| 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 12 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV013947053 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:54:53Z |
| institution | BVB |
| isbn | 0821821709 |
| language | English Russian |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009543668 |
| oclc_num | 45610139 |
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| owner | DE-355 DE-BY-UBR DE-703 DE-384 |
| owner_facet | DE-355 DE-BY-UBR DE-703 DE-384 |
| physical | X, 235 S. |
| publishDate | 2001 |
| publishDateSearch | 2001 |
| publishDateSort | 2001 |
| publisher | AMS |
| record_format | marc |
| series | Translations of mathematical monographs |
| series2 | Translations of mathematical monographs |
| spelling | Smirnov, Vladimir A. 1951- Verfasser (DE-588)10336627X aut Simplicialʹnye i operadnye metody v algebraičeskoj topologii Simplicial and operad methods in algebraic topology V. A. Smirnov Providence, RI AMS 2001 X, 235 S. txt rdacontent n rdamedia nc rdacarrier Translations of mathematical monographs 198 Aus d. Russ. übers. Algebraïsche structuren gtt Algebraïsche topologie gtt Structures algébriques ordonnées Structures algébriques ordonnées ram Topologie algébrique Topologie algébrique ram Algebraic topology Operads Ordered algebraic structures Algebraische Topologie (DE-588)4120861-4 gnd rswk-swf Geordnete algebraische Struktur (DE-588)4156743-2 gnd rswk-swf Algebraische Topologie (DE-588)4120861-4 s Geordnete algebraische Struktur (DE-588)4156743-2 s DE-604 Translations of mathematical monographs 198 (DE-604)BV000002394 198 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009543668&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Smirnov, Vladimir A. 1951- Simplicial and operad methods in algebraic topology Translations of mathematical monographs Algebraïsche structuren gtt Algebraïsche topologie gtt Structures algébriques ordonnées Structures algébriques ordonnées ram Topologie algébrique Topologie algébrique ram Algebraic topology Operads Ordered algebraic structures Algebraische Topologie (DE-588)4120861-4 gnd Geordnete algebraische Struktur (DE-588)4156743-2 gnd |
| subject_GND | (DE-588)4120861-4 (DE-588)4156743-2 |
| title | Simplicial and operad methods in algebraic topology |
| title_alt | Simplicialʹnye i operadnye metody v algebraičeskoj topologii |
| title_auth | Simplicial and operad methods in algebraic topology |
| title_exact_search | Simplicial and operad methods in algebraic topology |
| title_full | Simplicial and operad methods in algebraic topology V. A. Smirnov |
| title_fullStr | Simplicial and operad methods in algebraic topology V. A. Smirnov |
| title_full_unstemmed | Simplicial and operad methods in algebraic topology V. A. Smirnov |
| title_short | Simplicial and operad methods in algebraic topology |
| title_sort | simplicial and operad methods in algebraic topology |
| topic | Algebraïsche structuren gtt Algebraïsche topologie gtt Structures algébriques ordonnées Structures algébriques ordonnées ram Topologie algébrique Topologie algébrique ram Algebraic topology Operads Ordered algebraic structures Algebraische Topologie (DE-588)4120861-4 gnd Geordnete algebraische Struktur (DE-588)4156743-2 gnd |
| topic_facet | Algebraïsche structuren Algebraïsche topologie Structures algébriques ordonnées Topologie algébrique Algebraic topology Operads Ordered algebraic structures Algebraische Topologie Geordnete algebraische Struktur |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009543668&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000002394 |
| work_keys_str_mv | AT smirnovvladimira simplicialʹnyeioperadnyemetodyvalgebraiceskojtopologii AT smirnovvladimira simplicialandoperadmethodsinalgebraictopology |