Spaces of homotopy self-equivalences: a survey
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | German |
| Published: |
Berlin [u.a.]
Springer
1997
|
| Series: | Lecture notes in mathematics
1662 |
| Subjects: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007637483&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Physical Description: | IX, 170 S. |
| ISBN: | 3540631038 |
Staff View
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| 245 | 1 | 0 | |a Spaces of homotopy self-equivalences |b a survey |c John W. Rutter |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 1997 | |
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| 490 | 1 | |a Lecture notes in mathematics |v 1662 | |
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Record in the Search Index
| DE-BY-TUM_call_number | 0102 MAT 001z 2001 B 999-1662 |
|---|---|
| DE-BY-TUM_katkey | 850397 |
| DE-BY-TUM_location | 01 |
| DE-BY-TUM_media_number | 040020185820 |
| _version_ | 1821931175824850945 |
| adam_text | Contents
1 Preliminaries 1
2 Building blocks 4
2.1 Eilenberg MacLane spaces 4
2.2 Moore spaces 4
2.3 Finite presentability 6
3 Representations: homology and homotopy 7
4 Surfaces 11
4.1 Homeotopy and mapping class groups 12
4.2 Homology representations 14
4.3 Braid groups 16
4.4 Other properties 17
5 Generators: surface, modular groups 19
5.1 Twist homeomorphisms 19
5.2 Orientable surfaces 20
5.3 Non orientable surfaces 21
5.4 Low genus examples 22
5.5 Presentations of homeotopy groups 23
5.6 Braid groups 24
5.7 Free, free abelian, and symplectic groups 25
5.8 Torelli groups 26
6 Manifolds of dimension three or more 28
6.1 Thehomomorphism?T(M) f*(M) 28
6.2 Finite generation, finite presentation and finiteness .... 30
6.3 Relations between E{M), H{M) and Diff(M) 32
6.4 Generation of higher homotopy groups 33
7 £*{X) not finitely generated 34
8 Localization 36
9 £*(X) finitely presented, nilpotent 40
10 C K duality 44
11 Cellular/homology complexes: methods 45
VIII Contents
12 Cellular, homology complexes: calculations 54
12.1 Simply connected complexes with only two cells 54
12.2 Simply connected complexes: three or more cells 55
12.3 Products of spheres, sphere bundles over spheres 56
12.4 if spaces of low rank 59
12.5 Projective spaces 61
13 Non 1 connected Postnikov: methods 63
13.1 topM and based homotopy classes 63
13.2 Free homotopy classes 70
13.3 Historical development 71
13.4 Some simplifications 72
14 Homotopy systems, chain complexes 74
15 Non—1—connected spaces: calculations 80
15.1 (n, ro) complexes 81
15.2 Lens spaces of CA presentations 82
15.3 (n, ra) complexes: 7r finite 88
15.4 (tt, n) complexes: infinite n of finite Hirsch rank 92
15.5 Other examples 93
16 Whitehead torsion, simple homotopy 94
16.1 Spaces for which r is surjective 95
16.2 Spaces for which r is not surjective 96
16.3 The image t(^;i(P^)) 96
16.4 The pseudo projective planes 96
16.5 Finite (tt, n) complexes 97
17 Unions and products 98
17.1 The union of two/i coloops 98
17.2 Spaces of the form X = Mm(A) VM (f) 100
17.3 Spaces of the form Sm V X 102
17.4 The product of two /i loops 103
17.5 A product or union: one space an /i loop or /i coloop . . 105
17.6 The representation £*(X x 7) £*(*) x£*(Y) 106 .
17.7 Unions and products of n spaces (n 3) 107
17.8 Historical development 107
Contents IX
18 Group theoretic properties 108
18.1 Readability 108
18.2 Rigidity 109
18.3 Elements of order p and finiteness 109
18.4 Rank Ill
18.5 Non abelian nature Ill
18.6 Residual finiteness 112
19 Homotopy type, homotopy groups 113
19.1 The homotopy type of E{X) 113
19.2 Sections of e : E(X) » X 117
19.3 The image of 5, : ir?(X : 1) • n(X) 118
19.4 Rational homotopy groups 119
19.5 Nilpotent actions and finite type 119
20 Homotopy automorphisms of // spaces 121
20.1 Products of i/ spaces 122
20.2 //^spaces of finite rank 122
20.3 Group theoretic properties 123
21 Fibre and equivariant HE s 124
21.1 Fibre homotopy equivalences, classifying spaces 124
21.2 An exact sequence for calculation 126
21.3 Equivariant homotopy equivalences 127
21.4 Nilpotency, arithmeticity and uncountability 128
21.5 Equivalence of the theories 128
21.6 Calculations 129
22 Applications 130
22.1 Classification of spaces of the same n type for all n .... 130
22.2 Classification of fibre bundles and fibre spaces 131
22.3 Sets of rational homotopy type 133
Appendix A Arithmetic groups and commensurability 134
Appendix B Nilpotency, rank and group actions 135
References 138
List of notation 163
Index 165
|
| any_adam_object | 1 |
| author | Rutter, John W. 1935- |
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| dewey-ones | 510 - Mathematics |
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| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV011363502 |
| illustrated | Not Illustrated |
| indexdate | 2024-12-20T10:11:07Z |
| institution | BVB |
| isbn | 3540631038 |
| language | German |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007637483 |
| oclc_num | 246274473 |
| open_access_boolean | |
| owner | DE-20 DE-91G DE-BY-TUM DE-739 DE-824 DE-355 DE-BY-UBR DE-706 DE-634 DE-83 DE-188 DE-11 |
| owner_facet | DE-20 DE-91G DE-BY-TUM DE-739 DE-824 DE-355 DE-BY-UBR DE-706 DE-634 DE-83 DE-188 DE-11 |
| physical | IX, 170 S. |
| publishDate | 1997 |
| publishDateSearch | 1997 |
| publishDateSort | 1997 |
| publisher | Springer |
| record_format | marc |
| series | Lecture notes in mathematics |
| series2 | Lecture notes in mathematics |
| spellingShingle | Rutter, John W. 1935- Spaces of homotopy self-equivalences a survey Lecture notes in mathematics H-spaces Homotopy equivalences Homotopy groups Homotopieäquivalenz (DE-588)4160618-8 gnd Homotopiegruppe (DE-588)4160621-8 gnd Rationale Homotopietheorie (DE-588)4177003-1 gnd Algebraische Topologie (DE-588)4120861-4 gnd |
| subject_GND | (DE-588)4160618-8 (DE-588)4160621-8 (DE-588)4177003-1 (DE-588)4120861-4 |
| title | Spaces of homotopy self-equivalences a survey |
| title_auth | Spaces of homotopy self-equivalences a survey |
| title_exact_search | Spaces of homotopy self-equivalences a survey |
| title_full | Spaces of homotopy self-equivalences a survey John W. Rutter |
| title_fullStr | Spaces of homotopy self-equivalences a survey John W. Rutter |
| title_full_unstemmed | Spaces of homotopy self-equivalences a survey John W. Rutter |
| title_short | Spaces of homotopy self-equivalences |
| title_sort | spaces of homotopy self equivalences a survey |
| title_sub | a survey |
| topic | H-spaces Homotopy equivalences Homotopy groups Homotopieäquivalenz (DE-588)4160618-8 gnd Homotopiegruppe (DE-588)4160621-8 gnd Rationale Homotopietheorie (DE-588)4177003-1 gnd Algebraische Topologie (DE-588)4120861-4 gnd |
| topic_facet | H-spaces Homotopy equivalences Homotopy groups Homotopieäquivalenz Homotopiegruppe Rationale Homotopietheorie Algebraische Topologie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007637483&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000676446 |
| work_keys_str_mv | AT rutterjohnw spacesofhomotopyselfequivalencesasurvey |
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| Call Number: |
0102 MAT 001z 2001 B 999-1662
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