Homotopy type and homology:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Oxford
Clarendon Press
1996
|
| Schriftenreihe: | Oxford mathematical monographs
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XII, 489 S. graph. Darst. |
| ISBN: | 0198514824 |
Internformat
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| 245 | 1 | 0 | |a Homotopy type and homology |c Hans-Joachim Baues |
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Datensatz im Suchindex
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| adam_text | CONTENTS
Introduction 1
Chapter 1 Linear extension and Moore spaces 8
1.1 Detecting functors, linear extensions, and the cohomology of
categories 8
1.2 Whitehead s quadratic functor T 15
1.3 Moore spaces and homotopy groups with coefficients 18
1.4 Suspended pseudo projective planes 21
1.5 The homotopy category of Moore spaces M , n 3 23
1.6 Moore spaces and the category G 25
Chapter 2 Invariants of homotopy types 31
2.1 The Hurewicz homomorphism and Whitehead s certain exact
sequence 32
2.2 T groups with coefficients 40
2.3 An exact sequence for the Hurewicz homomorphism with
coefficients 45
2.4 Infinite symmetric products and Kan loop groups 51
2.5 Postnikov invariants of a homotopy type 54
2.6 Boundary invariants of a homotopy type 63
2.7 Homotopy decomposition and homology decomposition 72
2.8 Unitary invariants of a homotopy type 76
Chapter 3 On the classification of homotopy types 81
3.1 kype functors 81
3.2 bype functors 85
3.3 Duality of bype and kype 89
3.4 The classification theorem 97
3.5 The semitrivial case of the classification theorem and
Whitehead s classification 104
3.6 The split case of the classification theorem 107
3.7 Proof of the classification theorem 111
Chapter 4 The CW tower of categories 116
4.1 Exact sequences for functors 117
4.2 Homotopy systems of order (n + 1) 121
X CONTENTS
4.3 The CW tower of categories 124
4.4 Boundary invariants for homotopy systems 129
4.5 Three formulas for the obstruction operator 131
4.6 A Realizability 135
4.7 Proof of the boundary classification theorem 138
4.8 The computation of isotropy groups in the CW tower 143
Chapter 5 Spanier Whitehead duality and the stable
CW tower 149
5.1 Cohomotopy groups 149
5.2 Spanier Whitehead duality 152
5.3 Cohomology operations and homotopy groups 156
5.4 The stable CW tower and its dual 163
Chapter 6 Eilenberg Mac Lane and Moore functors 168
A Eilenberg Mac Lane functors 168
6.1 Homology of Eilenberg Mac Lane spaces 168
6.2 Some functors for abelian groups 170
6.3 Examples of Eilenberg Mac Lane functors 178
6.4 On (w — l) connected (n + l) dimensional homotopy types with
77,^=0 for m i n 181
6.5 Split Eilenberg Mac Lane functors 184
6.6 A transformation from homotopy groups of Moore spaces to
homology groups of Eilenberg Mac Lane spaces 186
B Moore functors 190
6.7 Moore types and Moore functors 191
6.8 On (m — l) connected (n + l) dimensional homotopy types X
with HtX = 0 for m i n 195
6.9 The stable case with trivial 2 torsion 196
6.10 Moore spaces and Spanier Whitehead duality 198
6.11 Homotopy groups of Moore spaces in the stable range 202
6.12 Stable and principal maps between Moore spaces 206
6.13 Quadratic Z modules 215
6.14 Quadratic derived functors 225
6.15 Metastable homotopy groups of Moore spaces 229
Chapter 7 The homotopy category of (n — 1) connected
(n + 1) types 239
7.1 A linear extension for types), 240
7.2 The enriched category of Moore spaces 244
CONTENTS xi
Chapter 8 On the homotopy classification of (n 1) connected
(n + 3) dimensional polyhedra, n 4 249
8.1 Algebraic models of (n l) connected (« + 3) dimensional
homotopy types, n 4 249
8.2 Omrn + 2M{A,n) 258
8.3 The group Fn + 2 of an (n — l) connected space, n 4 263
8.4 Proof of the classification theorem 8.1.6 267
8.5 Adem operations 269
Chapter 9 On the homotopy classification of 2 connected
6 dimensional polyhedra 277
9.1 Algebraic models of 2 connected 6 dimensional homotopy types 277
9.2 OmrsM(A,3) 286
9.3 Whitehead s group F5 of a 2 connected space 291
Chapter 10 Decomposition of homotopy types 294
10.1 The decomposition problem in representation theory and topology 294
10.2 The indecomposable (n — l) connected (n + 3) dimensional
polyhedra, n 4 298
10.3 The (n — l) connected (n + 3) dimensional polyedra with cyclic
homology groups, n 4 314
10.4 The decomposition problem for stable types 316
10.5 The (n l) connected (n + 2) types with cyclic homotopy
groups, n 4 320
10.6 Example: the truncated real projective spaces UPn + 4/UPn 327
10.7 The stable equivalence classes of 4 dimensional polyhedra and
simply connected 5 dimensional polyhedra 330
Chapter 11 Homotopy groups in dimension 4 333
11.1 On7r4A/(^,2) 333
11.2 Oni73U,M(B,2)) 344
11.3 On T4X and T3(B, X) 347
11.3A Appendix: nilization of TAX 354
11.4 On H3(B, K(A,2)) and difference homomorphisms 356
11.5 Elementary homotopy groups in dimension 4 361
11.6 The suspension of elementary homotopy groups in dimension 4 382
Chapter 12 On the homotopy classification of simply
connected 5 dimensional polyhedra 385
12.1 The groups G(q,A) 386
12.2 Homotopy groups with cyclic coefficients 392
12.2A Appendix: theories of cogroups and generalized homotopy groups 397
12.3 The functor T4 402
xii CONTENTS
12.4 The bifunctor T3 406
12.5 Algebraic models of 1 connected 5 dimensional homotopy types 412
12.6 The case tt3X=0 418
12.7 The case H2X uniquely 2 divisible 418
12.8 The case H2X free abelian 423
Appendix A Primary homotopy operations and homotopy
groups of mapping cones 425
A.1 Whitehead products 426
A.2 The James Hopf invariants 431
A.3 The fibre of the retraction Aw B *B and the Hilton Milnor
theorem 434
A.4 The loop space of a mapping cone 441
A.5 The fibre of a principal cofibration 444
A.6 EHP sequences 450
A.7 The operator Pg 456
A.8 The difference map V 463
A.9 The left distributivity law 471
A. 10 Distributivity laws of order 3 476
Bibliography 479
Notation for categories 485
Index 487
|
| any_adam_object | 1 |
| author | Baues, Hans J. 1943- |
| author_GND | (DE-588)128430702 |
| author_facet | Baues, Hans J. 1943- |
| author_role | aut |
| author_sort | Baues, Hans J. 1943- |
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| building | Verbundindex |
| bvnumber | BV010903005 |
| classification_rvk | SK 300 |
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| 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 |
| format | Book |
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| id | DE-604.BV010903005 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T18:00:52Z |
| institution | BVB |
| isbn | 0198514824 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007292428 |
| oclc_num | 845179029 |
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| physical | XII, 489 S. graph. Darst. |
| publishDate | 1996 |
| publishDateSearch | 1996 |
| publishDateSort | 1996 |
| publisher | Clarendon Press |
| record_format | marc |
| series2 | Oxford mathematical monographs |
| spelling | Baues, Hans J. 1943- Verfasser (DE-588)128430702 aut Homotopy type and homology Hans-Joachim Baues Oxford Clarendon Press 1996 XII, 489 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Oxford mathematical monographs Homologietheorie (DE-588)4141714-8 gnd rswk-swf Homotopietyp (DE-588)4160628-0 gnd rswk-swf CW-Komplex (DE-588)4148419-8 gnd rswk-swf Homotopietheorie (DE-588)4128142-1 gnd rswk-swf Homologietheorie (DE-588)4141714-8 s Homotopietheorie (DE-588)4128142-1 s DE-604 CW-Komplex (DE-588)4148419-8 s Homotopietyp (DE-588)4160628-0 s HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007292428&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Baues, Hans J. 1943- Homotopy type and homology Homologietheorie (DE-588)4141714-8 gnd Homotopietyp (DE-588)4160628-0 gnd CW-Komplex (DE-588)4148419-8 gnd Homotopietheorie (DE-588)4128142-1 gnd |
| subject_GND | (DE-588)4141714-8 (DE-588)4160628-0 (DE-588)4148419-8 (DE-588)4128142-1 |
| title | Homotopy type and homology |
| title_auth | Homotopy type and homology |
| title_exact_search | Homotopy type and homology |
| title_full | Homotopy type and homology Hans-Joachim Baues |
| title_fullStr | Homotopy type and homology Hans-Joachim Baues |
| title_full_unstemmed | Homotopy type and homology Hans-Joachim Baues |
| title_short | Homotopy type and homology |
| title_sort | homotopy type and homology |
| topic | Homologietheorie (DE-588)4141714-8 gnd Homotopietyp (DE-588)4160628-0 gnd CW-Komplex (DE-588)4148419-8 gnd Homotopietheorie (DE-588)4128142-1 gnd |
| topic_facet | Homologietheorie Homotopietyp CW-Komplex Homotopietheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007292428&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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