Strong shape and homology:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
2000
|
| Series: | Springer monographs in mathematics
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturverz. S. 465 - 477 |
| Physical Description: | XII, 489 S. graph. Darst. 24 cm |
| ISBN: | 3540661980 |
Staff View
MARC
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Record in the Search Index
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|---|---|
| adam_text | Table of Contents
Preface V
Introduction 1
I. COHERENT HOMOTOPY
1. Coherent mappings 9
1.1 Mappings of inverse systems 9
1.2 Coherent mappings of inverse systems 13
1.3 Composition of coherent mappings 23
1.4 The coherence operator C 26
2. Coherent homotopy 29
2.1 The coherent homotopy category CH(pro Top) 29
2.2 Associativity of the composition 34
2.3 The identity morphism 41
3. Coherent homotopy of sequences 47
3.1 Coherent homotopy of finite height 47
3.2 Coherent homotopy of inverse sequences 53
4. Coherent homotopy and localization 61
4.1 An isomorphism theorem in CH(pro Top) 61
4.2 Cotelescopes (homotopy limits) 72
4.3 Localizing pro Top at level homotopy equivalences 85
5. Coherent homotopy as a Kleisli category 93
5.1 The Kleisli category of a monad 93
5.2 CH(pro Top) is the Kleisli category of a monad 95
X Table of Contents
II. STRONG SHAPE
6. Resolutions 103
6.1 Resolutions of spaces and mappings 103
6.2 Characterization of resolutions 107
6.3 Resolutions versus limits 112
6.4 Existence of polyhedral and ANR resolutions 116
6.5 Resolutions of direct products and pairs 123
7. Strong expansions 129
7.1 Strong expansions of spaces 129
7.2 Resolutions are strong expansions 134
7.3 Invariance under coherent domination 138
8. Strong shape 147
8.1 Coherent expansions of spaces 147
8.2 The strong shape category 157
8.3 Strong shape equivalences 164
9. Strong shape of metric compacta 181
9.1 The Quigley strong shape category 181
9.2 Complement theorems 192
10. Selected results on strong shape 201
10.1 Normal pairs of spaces 201
10.2 Normal triads of spaces 202
10.3 Strong shape using the Vietoris system 204
10.4 The Bauer Giinther description of strong shape 205
10.5 Strong shape of compacta via multi valued maps 208
10.6 Strong shape using approximate systems 209
10.7 Strong shape and localization 210
10.8 Stable strong shape 211
III. HIGHER DERIVED LIMITS
11. The derived functors of lim 215
11.1 Inverse systems of modules 215
11.2 Projective and injective systems 221
11.3 lim and its right derived functors 228
11.4 Axiomatic characterization of the functors lim 240
11.5 Explicit formulae for lim71 244
11.6 lim for sequences 249
Table of Contents XI
12. lim™ and the extension functors Ext 253
12.1 The bifunctors Ext 253
12.2 Expressing lim in terms of Ext 262
13. The vanishing theorems 269
13.1 Homological dimension 269
13.2 Goblot s vanishing theorem 274
13.3 Systems with non vanishing lim 277
14. The cofinality theorem 285
14.1 Colimits and tensor products 285
14.2 The cofinality theorem for lim 291
15. Higher limits on the category pro Mod 301
15.1 lim 1 as a functor on pro Mod 301
15.2 Properties of lim on pro Mod 305
IV. HOMOLOGY GROUPS
16. Homology pro groups 319
16.1 Homology pro groups and Cech homology 319
16.2 Higher limits of homology pro groups 321
17. Strong homology groups of systems 327
17.1 Strong homology of pro chain complexes 327
17.2 The first Miminoshvili sequence 336
17.3 The second Miminoshvili sequence 342
17.4 Isomorphism theorems for strong homology 348
18. Strong homology on CH(pro Top) 353
18.1 Chain mappings induced by coherent mappings 353
18.2 Chain mappings induced by congruence classes 359
18.3 Chain mappings induced by homotopy classes 365
18.4 Chain mappings induced by composition 368
18.5 Induced chain mappings and the coherence functor 375
19. Strong homology of spaces 379
19.1 Strong homology groups of spaces 379
19.2 Strong excision property 383
19.3 Strong homology of clusters 388
19.4 Strong homology and dimension 394
19.5 Strong homology of polyhedra 396
19.6 Strong homology of metric compacta 399
XII Table of Contents
20. Spectral sequences. Abelian groups 405
20.1 The spectral sequence of a filtered complex 405
20.2 The spectral sequences of a bicomplex 413
20.3 The Roos spectral sequence 416
20.4 Pure extension functors Pext™ 422
20.5 Some theorems on abelian groups 427
21. Strong homology of compact spaces 439
21.1 Universal coefficients for compact polyhedra 439
21.2 Homology of compact spaces 443
21.3 Universal coefficients for compact spaces 446
21.4 A filtration of the strong homology group 448
21.5 Strong homology with compact supports 453
22. Generalized strong homology 459
References 465
List of Special Symbols 479
Author Index 483
Subject Index 485
|
| any_adam_object | 1 |
| author | Mardešić, Sibe 1927-2016 |
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| bvnumber | BV013023274 |
| 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 SK 320 |
| classification_tum | MAT 185f |
| ctrlnum | (OCoLC)42462796 (DE-599)BVBBV013023274 |
| 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 |
| format | Book |
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| illustrated | Illustrated |
| indexdate | 2024-07-09T18:37:50Z |
| institution | BVB |
| isbn | 3540661980 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-008872794 |
| oclc_num | 42462796 |
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| owner_facet | DE-355 DE-BY-UBR DE-91G DE-BY-TUM DE-634 DE-83 DE-11 |
| physical | XII, 489 S. graph. Darst. 24 cm |
| publishDate | 2000 |
| publishDateSearch | 2000 |
| publishDateSort | 2000 |
| publisher | Springer |
| record_format | marc |
| series2 | Springer monographs in mathematics |
| spelling | Mardešić, Sibe 1927-2016 Verfasser (DE-588)121368823 aut Strong shape and homology Sibe Mardešić Berlin [u.a.] Springer 2000 XII, 489 S. graph. Darst. 24 cm txt rdacontent n rdamedia nc rdacarrier Springer monographs in mathematics Literaturverz. S. 465 - 477 Forme, Théorie de la (Topologie) ram Homologie ram Homology theory Shape theory (Topology) Homologietheorie (DE-588)4141714-8 gnd rswk-swf Shape-Theorie (DE-588)4193842-2 gnd rswk-swf Shape-Theorie (DE-588)4193842-2 s Homologietheorie (DE-588)4141714-8 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008872794&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Mardešić, Sibe 1927-2016 Strong shape and homology Forme, Théorie de la (Topologie) ram Homologie ram Homology theory Shape theory (Topology) Homologietheorie (DE-588)4141714-8 gnd Shape-Theorie (DE-588)4193842-2 gnd |
| subject_GND | (DE-588)4141714-8 (DE-588)4193842-2 |
| title | Strong shape and homology |
| title_auth | Strong shape and homology |
| title_exact_search | Strong shape and homology |
| title_full | Strong shape and homology Sibe Mardešić |
| title_fullStr | Strong shape and homology Sibe Mardešić |
| title_full_unstemmed | Strong shape and homology Sibe Mardešić |
| title_short | Strong shape and homology |
| title_sort | strong shape and homology |
| topic | Forme, Théorie de la (Topologie) ram Homologie ram Homology theory Shape theory (Topology) Homologietheorie (DE-588)4141714-8 gnd Shape-Theorie (DE-588)4193842-2 gnd |
| topic_facet | Forme, Théorie de la (Topologie) Homologie Homology theory Shape theory (Topology) Homologietheorie Shape-Theorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008872794&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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