A user's guide to spectral sequences:
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cambridge
Univ. Press
2001
|
| Edition: | 2. ed. |
| Series: | Cambridge studies in advanced mathematics
58 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis Inhaltsverzeichnis |
| Item Description: | Hier auch später erschienene, unveränderte Nachdrucke |
| Physical Description: | XVI, 561 S. graph. Darst. |
| ISBN: | 0521561418 0521567599 |
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MARC
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| adam_text |
Table
of
Contents
Preface vii
Introduction 1X
Part
I: Algebra 1
1.
An Informai Introduction
3
1.1.
"There is
a spectral
sequence
." 3
1.2.
Lacunary
phenomena
1
1.3.
Exploiting further
structure
9
1.4.
Working backwards
19
1.5.
Interpreting the answer
23
2.
What is a Spectral Sequence?
28
2.1.
Definitions and basic properties
28
2.2.
How does a spectral sequence arise?
31
2.3.
Spectral sequences of algebras
44
2.4.
Algebraic applications
46
3.
Convergence of Spectral Sequences
61
3.1.
On convergence
61
3.2.
Limits and colimits
67
3.3.
Zeeman's comparison theorem
82
Part II: Topology
89
4.
Topological Background
91
4.1.
CW-complexes
92
4.2.
Simplicial sets
103
4.3.
Fibrations
109
4.4. Hopf
algebras and the Steenrod algebra
122
5.
The Leray-Serre spectral sequence I
133
5.1.
Construction of the spectral sequence
136
5.2.
Immediate applications
140
5.3.
Appendices
163
6.
The Leray-Serre spectral sequence II
180
6.1.
A proof of theorem
6.1 181
6.2.
The transgression
185
6.3.
Classifying spaces and characteristic classes
207
6.4.
Other constructions of the spectral sequence ®
221
7.
The Eilenberg-Moore Spectral Sequence I
232
7.1.
Differential homological algebra
234
7.2.
Bringing in the topology
248
Table of
Contents xv
7.3.
The Koszul
complex
257
7.4.
The homology of quotient spaces of group actions
265
8.
The Eilenberg-Moore Spectral Sequence II
273
8.1.
On homogeneous spaces
274
8.2.
Differentials in the Eilenberg-Moore spectral sequence
297
8.3.
Further structure
ЗІЗ
8bis.
Nontrivial
Fundamental Groups
329
8bls.
1.
Actions of the fundamental group
330
8bis.2. Homology of groups
334
8bls.3.
Nilpotent
spaces and groups
344
9.
The Adams Spectral Sequence
366
9.1.
Motivation: What cohomology sees
368
9.2.
More homological algebra; the functor Ext
376
9.3.
The spectral sequence
392
9.4.
Other geometric applications
407
9.5.
Computations
415
9.6.
Further structure
430
10.
The
Bockstein
spectral sequence
455
10.1.
The
Bockstein
spectral sequence
458
10.2.
Other
Bockstein
spectral sequences
480
Part III: Sins of Omission
485
11.
More Spectral Sequences in Topology
487
11.1.
Spectral sequences for mappings and spaces of mappings
487
11.2.
Spectral sequences and spectra
495
11.3.
Other Adams spectral sequences
499
11.4.
Equivariant matters
501
11.5.
Miscellanea
504
12.
Spectral sequences in Algebra, Geometry and Analysis
507
12.1.
Spectral sequences for rings and modules
507
12.2.
Spectral sequences in geometry
515
12.3.
Spectral sequences in algebraic K-theory
520
12.4.
Derived categories
523
Bibliography
525
Symbol Index
553
Index
555
Titel: A user's guide to spectral sequences
Autor: McCleary, John
Jahr: 2001
Table of Contents
Preface vu
Introduction 1X
Part I: Algebra 1
1. An Informal Introduction 3
1.1. "There is a spectral sequence . " 3
1.2. Lacunary phenomena 7
1.3. Exploiting further structure 9
1.4. Working backwards 19
1.5. Interpreting the answer 23
2. What is a Spectral Sequence? 28
2.1. Definitions and basic properties 28
2.2. How does a spectral sequence arise? 31
2.3. Spectral sequences of algebras 44
2.4. Algebraic applications 46
3. Convergence of Spectral Sequences 61
3.1. On convergence 61
3.2. Limits and colimits 67
3.3. Zeeman's comparison theorem 82
Part II: Topology 89
4. Topological Background 91
4.1. CW-complexes 92
4.2. Simplicial sets 103
4.3. Fibrations 109
4.4. Hopf algebras and the Steenrod algebra 122
5. The Leray-Serre spectral sequence I 133
5.1. Construction of the spectral sequence 136
5.2. Immediate applications 140
5.3. Appendices 163
6. The Leray-Serre spectral sequence II 180
6.1. A proof of theorem 6.1 181
6.2. The transgression 185
6.3. Classifying spaces and characteristic classes 207
6.4. Other constructions of the spectral sequence ® 221
7. The Eilenberg-Moore Spectral Sequence I 232
7.1. Differential homological algebra 234
7.2. Bringing in the topology 248
Table of Contents
xv
7.3. The Koszul complex 257
7.4. The homology of quotient spaces of group actions 265
8. The Eilenberg-Moore Spectral Sequence II 273
8.1. On homogeneous spaces 274
8.2. Differentials in the Eilenberg-Moore spectral sequence 297
8.3. Further structure 313
8bls. Nontrivial Fundamental Groups 329
8b,s. 1. Actions of the fundamental group 330
8bls.2. Homology of groups 334
8bls.3. Nilpotent spaces and groups 344
9. The Adams Spectral Sequence 366
9.1. Motivation: What cohomology sees 368
9.2. More homological algebra; the functor Ext 376
9.3. The spectral sequence 392
9.4. Other geometric applications 407
9.5. Computations 415
9.6. Further structure 430
10. The Bockstein spectral sequence 455
10.1. The Bockstein spectral sequence 458
10.2. Other Bockstein spectral sequences 480
Part III: Sins of Omission 485
11. More Spectral Sequences in Topology 487
11.1. Spectral sequences for mappings and spaces of mappings 487
11.2. Spectral sequences and spectra 495
11.3. Other Adams spectral sequences 499
11.4. Equivariant matters 501
11.5. Miscellanea 504
12. Spectral sequences in Algebra, Geometry and Analysis 507
12.1. Spectral sequences for rings and modules 507
12.2. Spectral sequences in geometry 515
12.3. Spectral sequences in algebraic K-theory 520
12.4. Derived categories 523
Bibliography 525
Symbol Index 553
Index 555 |
| any_adam_object | 1 |
| author | McCleary, John 1952- |
| author_GND | (DE-588)113779089 |
| author_facet | McCleary, John 1952- |
| author_role | aut |
| author_sort | McCleary, John 1952- |
| author_variant | j m jm |
| building | Verbundindex |
| bvnumber | BV013599303 |
| callnumber-first | Q - Science |
| callnumber-label | QA612 |
| callnumber-raw | QA612.8 |
| callnumber-search | QA612.8 |
| callnumber-sort | QA 3612.8 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SI 860 SK 320 |
| ctrlnum | (OCoLC)247428266 (DE-599)BVBBV013599303 |
| dewey-full | 514.2 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 514 - Topology |
| dewey-raw | 514.2 |
| dewey-search | 514.2 |
| dewey-sort | 3514.2 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 2. ed. |
| format | Book |
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| indexdate | 2024-12-13T11:10:54Z |
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| isbn | 0521561418 0521567599 |
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| series2 | Cambridge studies in advanced mathematics |
| spelling | McCleary, John 1952- Verfasser (DE-588)113779089 aut A user's guide to spectral sequences John McCleary 2. ed. Cambridge Univ. Press 2001 XVI, 561 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Cambridge studies in advanced mathematics 58 Hier auch später erschienene, unveränderte Nachdrucke Lévinas, Emmanuel 1906-1995 (DE-588)118572350 gnd rswk-swf Strauss, Leo 1899-1973 (DE-588)118833901 gnd rswk-swf Spektralsequenz Politische Philosophie (DE-588)4076226-9 gnd rswk-swf Spektralsequenz (DE-588)4182172-5 gnd rswk-swf 1\p (DE-588)4113937-9 Hochschulschrift gnd-content Spektralsequenz (DE-588)4182172-5 s DE-604 Strauss, Leo 1899-1973 (DE-588)118833901 p Politische Philosophie (DE-588)4076226-9 s Lévinas, Emmanuel 1906-1995 (DE-588)118572350 p Cambridge studies in advanced mathematics 58 (DE-604)BV000003678 58 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009288895&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009288895&sequence=000003&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | McCleary, John 1952- A user's guide to spectral sequences Cambridge studies in advanced mathematics Lévinas, Emmanuel 1906-1995 (DE-588)118572350 gnd Strauss, Leo 1899-1973 (DE-588)118833901 gnd Spektralsequenz Politische Philosophie (DE-588)4076226-9 gnd Spektralsequenz (DE-588)4182172-5 gnd |
| subject_GND | (DE-588)118572350 (DE-588)118833901 (DE-588)4076226-9 (DE-588)4182172-5 (DE-588)4113937-9 |
| title | A user's guide to spectral sequences |
| title_auth | A user's guide to spectral sequences |
| title_exact_search | A user's guide to spectral sequences |
| title_full | A user's guide to spectral sequences John McCleary |
| title_fullStr | A user's guide to spectral sequences John McCleary |
| title_full_unstemmed | A user's guide to spectral sequences John McCleary |
| title_short | A user's guide to spectral sequences |
| title_sort | a user s guide to spectral sequences |
| topic | Lévinas, Emmanuel 1906-1995 (DE-588)118572350 gnd Strauss, Leo 1899-1973 (DE-588)118833901 gnd Spektralsequenz Politische Philosophie (DE-588)4076226-9 gnd Spektralsequenz (DE-588)4182172-5 gnd |
| topic_facet | Lévinas, Emmanuel 1906-1995 Strauss, Leo 1899-1973 Spektralsequenz Politische Philosophie Hochschulschrift |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009288895&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009288895&sequence=000003&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000003678 |
| work_keys_str_mv | AT mcclearyjohn ausersguidetospectralsequences |
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