Geometry and topology of configuration spaces:
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
2001
|
| Series: | Springer monographs in mathematics
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XVI, 313 S. graph. Darst. |
| ISBN: | 3540666699 |
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MARC
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| 100 | 1 | |a Fadell, Edward R. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Geometry and topology of configuration spaces |c Edward R. Fadell ; Sufian Y. Husseini |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 2001 | |
| 300 | |a XVI, 313 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Springer monographs in mathematics | |
| 650 | 7 | |a Algebraïsche topologie |2 gtt | |
| 650 | 4 | |a Espace de configuration | |
| 650 | 4 | |a Topologie algébrique | |
| 650 | 4 | |a Algebraic topology | |
| 650 | 4 | |a Configuration space | |
| 650 | 0 | 7 | |a Konfigurationsraum |0 (DE-588)4199256-8 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Algebraische Topologie |0 (DE-588)4120861-4 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Konfigurationsraum |0 (DE-588)4199256-8 |D s |
| 689 | 0 | 1 | |a Algebraische Topologie |0 (DE-588)4120861-4 |D s |
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| 700 | 1 | |a Husseini, Sufian Y. |e Verfasser |4 aut | |
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Record in the Search Index
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|---|---|
| adam_text | Contents
Preface vii
Part I. The Homotopy Theory of
Configuration Spaces
Introduction 3
I. Basic Fibrations 5
1 The Projection proj^,. : Ffc(M) Fr(M) 6
2 Relations to Homogeneous Spaces G/H 9
3 The Pull back to 0n+i,r 10
4 Ffc_i,i(K +1) Restricted to On+1,r 11
5 Historical Remarks 12
II. Configuration Space of K +1, n 1 13
1 Filtration of Ffc(Mn+1) 14
2 Action of Ek 18
3 The Y B Relations 20
4 Filtration of 7r.(Ffc(Kn+1)) 21
5 When Are the Canonical Fibrations Trivial? 24
6 Historical Remarks 28
III. Configuration Spaces of Sn+1, n 1 29
1 Filtration of 7r»(F*+i(Sn+1)), n 1 31
2 Relation with Ffc(K +1) 33
3 The Groups irn, 7rn+i, (n + 1) Odd 37
4 Symmetry Invariance of Sk+i 38
5 The Y B Relations, (n + 1) Odd 41
6 The Dirac Class Ak+i 45
7 The Lie Algebra 7r»(Fr(5n+1)), n 1 49
8 Are The Canonical Fibrations Trivial? 52
9 Historical Remarks 55
xiv Contents
IV. The Two Dimensional Case 57
1 Asphericity of Ffc(R2) 58
2 Generators for 7n(Ffc(R2),q) 59
3 The Action of Ek on Ffc(R2) 63
4 The Y B Relations 69
5 A Presentation of 7Ti(Ffc(R2), q) 73
6 When Are the Canonical Fibrations Trivial? 81
7 The Group TriCFfc+iCS 2),^) 84
8 Historical Remarks 89
Part II. Homology and Cohomology of Ffc(M)
Introduction 93
V. The Algebra H*(Ffc(M);Z) 95
1 The Group H*(Wk(Rn+1); Z) 96
2 Invariance Under Ek 100
3 The Cohomological Y B Relations 101
4 The Structure of H*(¥k(Rn+1)) 103
5 The group Hn(Fk+1(Sn+1)) 105
6 H*(¥k+1(Sn+1)) as an ^(Fa^+^ Module Ill
7 The Algebra H*(Wk+l{Sn+l)), n + 1 Even 112
8 The Algebra iJ*(Ffc+1(Sn+1)), n + 1 Odd 113
9 Historical Remarks 115
VI. Cellular Models 117
1 A Model for F3(Rn+1) 121
2 The Twisted Product Structure on /f»(Ffc_r,r) 126
3 Perturbation and Affine Maps 127
4 An Illustrated Example 133
5 Multispherical Cycles 134
6 Twisted Products in #*(Ffc+1(,Sn+1)), n + 1 Odd 137
7 Twisted Products in tf«(Ffc+i(Sn+1)), n + 1 Even 141
8 The Cellular Structure of Ffc(Rn+1),n 1 143
9 The Cellular Structure of Ffc+i(5n+1) 147
10 The Cellular Structure of Ffc(R2) 149
11 The Cellular Structure for Ffc+1(52) 151
12 Historical Remarks 151
VII. Cellular Chain Models 153
1 Cellular Chain Coalgebras 153
2 The Coalgebra of Ffc(Rn+1) 155
3 The Coalgebra of Fk+l{Sn+1), (n+1) Odd 157
4 The Coalgebra C.(Y), Y ~ Ffc+1(5 +1), (n + 1) Even 161
Contents xv
Part III. Homology and Cohomology of Loop Spaces
Introduction 167
VIII. The Algebra H.(fl¥k{M))) 171
1 The Coalgebra if»(OFfc_r,r) 172
2 The Primitives in #*(J?Ffc_rir) 174
3 The Hopf Algebra H,((7FkJr r) 177
4 The Algebra H,(nWk+1(Sn+i)), (n + 1) Odd 180
5 The Algebra H,(nWk+1(Sn+l)), (n + 1) Even 182
6 Historical Remarks 185
IX. RPT Constructions 187
1 RPT Models for O(X) 188
2 Homotopy Inverse for M(X) 194
3 An RPT Model for A(X) 196
4 An RPT Model for Aa(X) 201
5 A Cellular Spectral Sequence 204
6 Historical Remarks 206
X. Cellular Chain Algebra Models 207
1 The Adams Hilton Algebra 207
2 An RPT model for 0(11™ i $) 210
3 C,(M(Xk r,r)), Xk r,r a Ffc_r,r 215
4 C.(M{Yk+l), Yk+1 ~ Ft+i(5B+1), (n + 1) Odd 217
5 C,(M(Y)), Y ~ Ffc+1(Sn+1), (n + 1) Even 219
6 The Eilenberg Moore Spectral Sequence of A(M) 220
XI. The Serre Spectral Sequence 225
1 The Case of Ffc_r,r, n 1 225
2 The Case of Ffc+i(S(n+1 ), (n + 1) Odd 234
3 The Case of Ffc+i(5n+1), (n + 1) Even 240
XII. Computation of H.(A(M)) 243
1 Splitting of #,(ylF*(Rn+1);Z2) 244
2 Coproducts in i/.(AF3(Rn+1);Z2) 254
3 The Growth of H,(A(R^ ) 257
4 The Growth of H.(/lFfc(R l+1)) 261
5 Cup Length in F (/l(Ffc_r.,r);Z2) 265
6 Historical Remarks 267
xvi Contents
XIII. / Category and Ends 269
1 Relative Category 270
2 Ends in W^2(R3(n+1 ) 274
3 T category 283
4 Strongly Admissible Sets 284
5 Historical Notes 290
XIV. Problems of fc body Type 293
1 Analytic Ends 294
2 The First Example 296
3 The Second Example 299
4 Historical Remarks 303
References 305
Index 311
|
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| indexdate | 2024-07-09T18:45:26Z |
| institution | BVB |
| isbn | 3540666699 |
| language | English |
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| physical | XVI, 313 S. graph. Darst. |
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| spelling | Fadell, Edward R. Verfasser aut Geometry and topology of configuration spaces Edward R. Fadell ; Sufian Y. Husseini Berlin [u.a.] Springer 2001 XVI, 313 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Springer monographs in mathematics Algebraïsche topologie gtt Espace de configuration Topologie algébrique Algebraic topology Configuration space Konfigurationsraum (DE-588)4199256-8 gnd rswk-swf Algebraische Topologie (DE-588)4120861-4 gnd rswk-swf Konfigurationsraum (DE-588)4199256-8 s Algebraische Topologie (DE-588)4120861-4 s DE-604 Husseini, Sufian Y. Verfasser aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009151906&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Fadell, Edward R. Husseini, Sufian Y. Geometry and topology of configuration spaces Algebraïsche topologie gtt Espace de configuration Topologie algébrique Algebraic topology Configuration space Konfigurationsraum (DE-588)4199256-8 gnd Algebraische Topologie (DE-588)4120861-4 gnd |
| subject_GND | (DE-588)4199256-8 (DE-588)4120861-4 |
| title | Geometry and topology of configuration spaces |
| title_auth | Geometry and topology of configuration spaces |
| title_exact_search | Geometry and topology of configuration spaces |
| title_full | Geometry and topology of configuration spaces Edward R. Fadell ; Sufian Y. Husseini |
| title_fullStr | Geometry and topology of configuration spaces Edward R. Fadell ; Sufian Y. Husseini |
| title_full_unstemmed | Geometry and topology of configuration spaces Edward R. Fadell ; Sufian Y. Husseini |
| title_short | Geometry and topology of configuration spaces |
| title_sort | geometry and topology of configuration spaces |
| topic | Algebraïsche topologie gtt Espace de configuration Topologie algébrique Algebraic topology Configuration space Konfigurationsraum (DE-588)4199256-8 gnd Algebraische Topologie (DE-588)4120861-4 gnd |
| topic_facet | Algebraïsche topologie Espace de configuration Topologie algébrique Algebraic topology Configuration space Konfigurationsraum Algebraische Topologie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009151906&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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