Abstract homotopy and simple homotopy theory:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Singapore [u.a.]
World Scientific
1997
|
| Edition: | 1. publ. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | IX, 462 S. graph. Darst. |
| ISBN: | 9810216025 |
Staff View
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Record in the Search Index
| _version_ | 1804142004195557376 |
|---|---|
| adam_text | CONTENTS
Introduction vii
I. Abstract homotopy theory 1
1. Why abstract homotopy theory? 1
2. Cylinders and cofibrations 2
3. Cocylinders and fibrations 12
4. Richer structure on cylinders 15
5. Cubical enrichment and Kan conditions 19
6. Dold s theorem 33
7. Gluing homotopy equivalences 47
8. Additive abstract homotopy theories 60
II. Homotopical algebra 76
1. Quillen type theories 77
2. Homotopy theory in categories of cofibrant objects 88
3. Duality 118
4. Additive abstract homotopy and categories of cofibrant
objects 133
III. Case studies 145
1. Groupoids 146
2. Simplicial sets and related examples 159
3. Chain complexes 207
4. Enriched categories 228
5. Additive cylinders 246
v
IV. Groupoid enrichment and track homotopy 253
1. Fundamental groupoid, groupoid enrichment, and Vogt s
lemma 253
2. Track homotopy categories and Dold s theorem 278
3. Exact sequences 291
V. Homotopy coherence 307
1. The idea of homotopy coherence 307
2. The simplicial version of homotopy coherence 317
3. Homotopy limits and colimits 334
VI. Abstract simple homotopy theories 342
1. Simple homotopy theory 342
2. Eckmann-Siebenmann abstract simple homotopy theory 345
3. Generation of simple homotopy equivalences 358
4. The mapping cylinder calculus 364
VII. Injective simple homotopy theories 402
1. Simple equivalences in injective simple homotopy theory 402
2. The group E(X) 411
3. Examples 416
4. Finitely generated relatively injective 7L [C2]-modules 420
5. Open examples and problems 427
Glossary of terms from category theory 429
References 447
Index 455
vi
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| any_adam_object | 1 |
| author | Kamps, Klaus Heiner 1941-2019 Porter, Timothy 1947- |
| author_GND | (DE-588)172179262 (DE-588)172311950 |
| author_facet | Kamps, Klaus Heiner 1941-2019 Porter, Timothy 1947- |
| author_role | aut aut |
| author_sort | Kamps, Klaus Heiner 1941-2019 |
| author_variant | k h k kh khk t p tp |
| building | Verbundindex |
| bvnumber | BV024974695 |
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| ctrlnum | (OCoLC)833034893 (DE-599)BVBBV024974695 |
| 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 | 3514.24 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 1. publ. |
| format | Book |
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| id | DE-604.BV024974695 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T22:24:52Z |
| institution | BVB |
| isbn | 9810216025 |
| language | English |
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| physical | IX, 462 S. graph. Darst. |
| publishDate | 1997 |
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| publishDateSort | 1997 |
| publisher | World Scientific |
| record_format | marc |
| spelling | Kamps, Klaus Heiner 1941-2019 Verfasser (DE-588)172179262 aut Abstract homotopy and simple homotopy theory K. H. Kamps ; T. Porter 1. publ. Singapore [u.a.] World Scientific 1997 IX, 462 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Homotopietheorie (DE-588)4128142-1 gnd rswk-swf Homotopietheorie (DE-588)4128142-1 s DE-604 Porter, Timothy 1947- Verfasser (DE-588)172311950 aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=019642219&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Kamps, Klaus Heiner 1941-2019 Porter, Timothy 1947- Abstract homotopy and simple homotopy theory Homotopietheorie (DE-588)4128142-1 gnd |
| subject_GND | (DE-588)4128142-1 |
| title | Abstract homotopy and simple homotopy theory |
| title_auth | Abstract homotopy and simple homotopy theory |
| title_exact_search | Abstract homotopy and simple homotopy theory |
| title_full | Abstract homotopy and simple homotopy theory K. H. Kamps ; T. Porter |
| title_fullStr | Abstract homotopy and simple homotopy theory K. H. Kamps ; T. Porter |
| title_full_unstemmed | Abstract homotopy and simple homotopy theory K. H. Kamps ; T. Porter |
| title_short | Abstract homotopy and simple homotopy theory |
| title_sort | abstract homotopy and simple homotopy theory |
| topic | Homotopietheorie (DE-588)4128142-1 gnd |
| topic_facet | Homotopietheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=019642219&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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