The topological classification of stratified spaces:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Chicago u.a.
Univ. of Chicago Press
1994
|
| Series: | Chicago lectures in mathematics series
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIII, 283 S. Ill., graph. Darst. |
| ISBN: | 0226885666 0226885674 |
Staff View
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| 245 | 1 | 0 | |a The topological classification of stratified spaces |c Shmuel Weinberger |
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Record in the Search Index
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| adam_text | Contents
Preface xi
0. Introduction 1
0.1. Classification of manifolds 1
0.2. Topological manifolds 5
0.3. Stratified spaces 7
0.4. Some examples 9
0.5. A word about methods 13
PART I. THE THEORY OF MANIFOLDS 17
1. Algebraic K theory and topology 19
1.1. Wall s finiteness obstruction 19
1.2. Simple homotopy theory 22
I.2.A. Reidemeister torsion and analytic torsion 25
1.3. Handlebody theory 28
1.4. Completing noncompact manifolds 31
1.5. The A cobordism theorem 33
1.5.A. Proper A cobordism theorem 36
1.6. Some useful formulae 37
1.7. Some applications 40
1.8. Notes 42
2. Surgery theory 45
2.1. Poincare duality 45
2.2. Spivak fibration 48
2.3. Reducibility and normal invariants 50
2.4. The surgery exact sequence 51
2.4.A. The Rothenberg sequences 59
2.4.B. Proper surgery 60
2.5. F/ Top and the characteristic variety theorem 61
2.5 .A. The signature operator and Sullivan orientations 64
2.5.B. Rochlin s theorem and F/PL 65
vii
viii Contents
2.5.C. F/O 67
2.6. Notes 68
3. Spacification and functoriality 70
3.1. Spacification 70
3.2. Blocked surgery 73
3.3. Algebraic theory of surgery 75
3.3.A. The structure of L spectra 79
3.4. Applications to manifold surgery 80
3.5. Notes 83
4. Applications 86
4.1. Homotopy CP s 87
4.2. Simply connected manifolds 90
4.3. Browder s splitting theorem 91
4.4. Embedding theory 93
4.5. Extension of group actions 95
4.6. Farrell fibering and Shaneson s formula 96
4.6.A. The Novikov conjecture 99
4.7. Homotopy lens spaces 104
4.7.A. Eta invariants 108
4.8. The space form problem 110
PART II. THE GENERAL THEORY OF STRATIFIED SPACES 113
5. Definitions and examples 115
5.1. Stratified spaces 115
5.2. Transversalities 120
5.3. Examples 122
5.4. Notes 125
6. Classification of stratified spaces 126
6.1. PL classification 127
6.2. Topological classification 131
6.2.A. Homology with coefficients in a cosheaf of
spectra 135
6.3. Notes 137
7. Transverse stratified classification 139
7.1. Browder Quinn theory 139
7.2. Notes 141
8. PT category 143
8.1. Surgery obstructions for homotopy transverse
maps 143
Contents ix
8.2. Homology as cohomology with vanishing
conditions 145
8.3. The inductive proof 146
9. Controlled topology 148
9.1. The bounded and controlled categories 150
9.2. Geometric algebra 153
9.3. Recognition as homology 156
9.4. Selected applications 161
9.4.A. Index theory on noncompact manifolds 167
9.4.B. The rigidity package for infranilmanifolds 175
9.4.C. The Grove Peterson Wu finiteness theorem 176
9.4.D. Homology manifolds 178
10. Proof of main theorems in Top 182
10.1. The /j corbordism theorem 182
10.2. Stable surgery 184
10.3. Destabilization 187
10.3.A. The structure of neighborhoods 188
PART III. APPLICATIONS 191
11. Manifolds and embedding theory revisited 193
11.1. Manifolds with boundary 193
11.2. Isolated singularities 194
11.3. Embedding theory 196
11.4. Immersions 199
11.5. On codimensions one and two 200
12. Supernormal spaces and varieties 202
12.1. Supernormal spaces 202
12.2. Intersection homology 204
12.3. Characteristic classes of self dual sheaves 209
12.3.A. Applications of Witt spaces 210
12.4. Spaces with only even codimensional strata 213
12.4.A. The BBDG decomposition theorem and
its application to characteristic classes
of singular varieties 214
13. Group actions 217
13.1. Remarks on the foundational theorems
of manifolds 218
13.2. Equivariant surgery for finite group actions 221
13.3. Locally free compact actions 228
x Contents
13.4. Nonlinear similarity 230
13.5. Replacement theorems 233
13.6. Semifree actions 237
14. Rigidity conjectures 241
14.1. Motivation 241
14.2. Variant forms of the conjecture 245
14.3. Evidence 254
14.4. Applications 260
Bibliography 265
Index 279
|
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| id | DE-604.BV010183085 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T17:47:58Z |
| institution | BVB |
| isbn | 0226885666 0226885674 |
| language | English |
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| physical | XIII, 283 S. Ill., graph. Darst. |
| publishDate | 1994 |
| publishDateSearch | 1994 |
| publishDateSort | 1994 |
| publisher | Univ. of Chicago Press |
| record_format | marc |
| series2 | Chicago lectures in mathematics series |
| spelling | Weinberger, Shmuel Verfasser aut The topological classification of stratified spaces Shmuel Weinberger Chicago u.a. Univ. of Chicago Press 1994 XIII, 283 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Chicago lectures in mathematics series Espaces topologiques ram Variétés topologiques ram Topological manifolds Topological spaces Topologische Mannigfaltigkeit (DE-588)4185712-4 gnd rswk-swf Topologischer Raum (DE-588)4137586-5 gnd rswk-swf Topologischer Raum (DE-588)4137586-5 s DE-604 Topologische Mannigfaltigkeit (DE-588)4185712-4 s HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006764848&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Weinberger, Shmuel The topological classification of stratified spaces Espaces topologiques ram Variétés topologiques ram Topological manifolds Topological spaces Topologische Mannigfaltigkeit (DE-588)4185712-4 gnd Topologischer Raum (DE-588)4137586-5 gnd |
| subject_GND | (DE-588)4185712-4 (DE-588)4137586-5 |
| title | The topological classification of stratified spaces |
| title_auth | The topological classification of stratified spaces |
| title_exact_search | The topological classification of stratified spaces |
| title_full | The topological classification of stratified spaces Shmuel Weinberger |
| title_fullStr | The topological classification of stratified spaces Shmuel Weinberger |
| title_full_unstemmed | The topological classification of stratified spaces Shmuel Weinberger |
| title_short | The topological classification of stratified spaces |
| title_sort | the topological classification of stratified spaces |
| topic | Espaces topologiques ram Variétés topologiques ram Topological manifolds Topological spaces Topologische Mannigfaltigkeit (DE-588)4185712-4 gnd Topologischer Raum (DE-588)4137586-5 gnd |
| topic_facet | Espaces topologiques Variétés topologiques Topological manifolds Topological spaces Topologische Mannigfaltigkeit Topologischer Raum |
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