Classifying spaces of sporadic groups:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Providence, Rhode Island
American Mathematical Society
[2008]
|
| Series: | Mathematical surveys and monographs
Volume 147 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | xvi, 289 Seiten Diagramme |
| ISBN: | 9780821844748 |
Staff View
MARC
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| 100 | 1 | |a Benson, David J. |d 1955- |e Verfasser |0 (DE-588)110324714 |4 aut | |
| 245 | 1 | 0 | |a Classifying spaces of sporadic groups |c David J. Benson, Stephen D. Smith |
| 264 | 1 | |a Providence, Rhode Island |b American Mathematical Society |c [2008] | |
| 264 | 4 | |c © 2008 | |
| 300 | |a xvi, 289 Seiten |b Diagramme | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Mathematical surveys and monographs |v Volume 147 | |
| 650 | 4 | |a Sporadic groups (Mathematics) | |
| 650 | 4 | |a Classifying spaces | |
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| 830 | 0 | |a Mathematical surveys and monographs |v Volume 147 |w (DE-604)BV000018014 |9 147 | |
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Record in the Search Index
| _version_ | 1804137907762495488 |
|---|---|
| adam_text | Contents
Introduction
ix
Some general notation and conventions
xiii
Chapter
1.
Overview of our main results
1
Part
1.
Exposition of background material
5
Chapter
2.
Review of selected aspects of group cohomology
7
2.1.
Some features of group cohomology via the algebraic approach
7
2.2.
Some features of group cohomology via the classifying space
9
2.3.
The relation between the coefficient rings
Z
and Fp
12
2.4.
The duality relation between homology and cohomology
14
2.5.
The
Borei
construction and G-equivariant homology
16
2.6.
Spectral sequences for G-equivariant homology
20
2.7.
Review of some aspects of simplicial complexes
23
Chapter
3.
Simplicial sets and their equivalence with topological spaces
27
3.1.
The context of simplicial sets
27
3.2.
A presentation for the category
Δ
of finite ordered sets
29
3.3.
Singular simplices and geometric realization
30
3.4.
Products and function spaces
32
3.5.
Categorical settings for homotopy theory
35
3.6.
Model categories. Kan complexes and Quillen s equivalence
36
3.7.
Simplicial
Я
-modules
and homology
40
Chapter
4.
Bousfield-Kan completions and homotopy colimits
43
4.1.
Cosimplicial objects
43
4.2.
Bousfield-Kan completions
45
4.3.
Completion of the classifying space BG
48
4.4.
Simplicial spaces
50
4.5.
Diagrams of spaces and homotopy colimits
52
4.6.
The homotopy colimit over a simplex category
61
4.7.
The
Borei
construction as a homotopy colimit
65
4.8.
The Bousfield-Kan homology spectral sequence
67
Chapter
5.
Decompositions and ample collections of p-subgroups
73
5.1.
Some history of homology and homotopy decompositions
74
5.2.
Homology decompositions defined by homotopy colimits
83
5.3.
Ampleness for collections of subgroups
87
5.4.
The centralizer decomposition
89
vi
CONTENTS
5.5.
The subgroup decomposition
90
5.6.
The normalizer decomposition
92
5.7.
Ampleness for the centric collection
99
5.8.
Sharpness for the three decompositions
100
5.9.
The standard ample G-homotopy type defined by SP(G)
103
5.10.
Ample (but potentially inequivalent)
subcollections
of AP(G)
106
5.11.
Ample (but potentially inequivalent)
subcollections
of BP(G)
107
Chapter
6.
2-local geometries for simple groups
109
6.1.
Some history of geometries for simple groups
110
6.2.
Preview: some initial examples of local geometries
113
6.3.
Some general constructions of 2-local geometries
126
6.4.
Flag-transitive action on geometries
136
6.5.
Some equivalence methods for 2-local geometries
142
6.6.
Final remarks on 2-local geometries
150
Part
2.
Main results on sporadic groups
153
Chapter
7.
Decompositions for the individual sporadic groups
155
7.1.
The
Mathieu
group
Л/ц
157
7.2.
The
Mathieu
group M12
161
7.3.
The
Mathieu
group
M
22 165
7.4.
The
Mathieu
group M23
172
7.5.
The
Mathieu
group M24
178
7.6.
The
Janko
group J
180
7.7.
The
Janko
group J2
181
7.8.
The
Janko
group
Ą
183
7.9.
The
Janko
group J4
187
7.10.
The Higman-Sims group
HS 190
7.11.
The McLaughlin group McL
194
7.12.
The Suzuki group
5 иг
197
7.13.
The Conway group Co.-j
200
7.14.
The Conway group Co2
203
7.15.
The Conway group Co
206
7.16.
The Fischer group Fi22
208
7.17.
The Fischer group Fi2z
211
7.18.
The Fischer group Fi 2i
215
7.19.
The Haiada-Norton group HN
=
F5
222
7.20.
The Thompson group Th
=
F3
224
7.21.
The Baby Monster
В
=
F2
226
7.22.
The Fischer-Griess Monster
M
=
Fi
229
7.23.
The Held group He
231
7.24.
The Rudvalis group Ru
233
7.25.
The O Nan group
О Л
237
7.26.
The Lyons group Ly
242
Chapter
8.
Details of proofs for individual groups
247
8.1.
Details for Mi2
247
8.2.
Details for J:}
249
CONTENTS
8.3.
Details
for
HS
8.4.
Details
for
Fi22
8.5.
Details
for
FÏ24.
8.6.
Details
for
ΗΝ
8.7.
Details
for
Ru
8.8.
Details
for
Ο Ν
Bibliography
Index
250
253
255
264
265
272
275
281
|
| adam_txt |
Contents
Introduction
ix
Some general notation and conventions
xiii
Chapter
1.
Overview of our main results
1
Part
1.
Exposition of background material
5
Chapter
2.
Review of selected aspects of group cohomology
7
2.1.
Some features of group cohomology via the algebraic approach
7
2.2.
Some features of group cohomology via the classifying space
9
2.3.
The relation between the coefficient rings
Z
and Fp
12
2.4.
The duality relation between homology and cohomology
14
2.5.
The
Borei
construction and G-equivariant homology
16
2.6.
Spectral sequences for G-equivariant homology
20
2.7.
Review of some aspects of simplicial complexes
23
Chapter
3.
Simplicial sets and their equivalence with topological spaces
27
3.1.
The context of simplicial sets
27
3.2.
A presentation for the category
Δ
of finite ordered sets
29
3.3.
Singular simplices and geometric realization
30
3.4.
Products and function spaces
32
3.5.
Categorical settings for homotopy theory
35
3.6.
Model categories. Kan complexes and Quillen's equivalence
36
3.7.
Simplicial
Я
-modules
and homology
40
Chapter
4.
Bousfield-Kan completions and homotopy colimits
43
4.1.
Cosimplicial objects
43
4.2.
Bousfield-Kan completions
45
4.3.
Completion of the classifying space BG
48
4.4.
Simplicial spaces
50
4.5.
Diagrams of spaces and homotopy colimits
52
4.6.
The homotopy colimit over a simplex category
61
4.7.
The
Borei
construction as a homotopy colimit
65
4.8.
The Bousfield-Kan homology spectral sequence
67
Chapter
5.
Decompositions and ample collections of p-subgroups
73
5.1.
Some history of homology and homotopy decompositions
74
5.2.
Homology decompositions defined by homotopy colimits
83
5.3.
Ampleness for collections of subgroups
87
5.4.
The centralizer decomposition
89
vi
CONTENTS
5.5.
The subgroup decomposition
90
5.6.
The normalizer decomposition
92
5.7.
Ampleness for the centric collection
99
5.8.
Sharpness for the three decompositions
100
5.9.
The "standard" ample G-homotopy type defined by SP(G)
103
5.10.
Ample (but potentially inequivalent)
subcollections
of AP(G)
106
5.11.
Ample (but potentially inequivalent)
subcollections
of BP(G)
107
Chapter
6.
2-local geometries for simple groups
109
6.1.
Some history of geometries for simple groups
110
6.2.
Preview: some initial examples of local geometries
113
6.3.
Some general constructions of 2-local geometries
126
6.4.
Flag-transitive action on geometries
136
6.5.
Some equivalence methods for 2-local geometries
142
6.6.
Final remarks on 2-local geometries
150
Part
2.
Main results on sporadic groups
153
Chapter
7.
Decompositions for the individual sporadic groups
155
7.1.
The
Mathieu
group
Л/ц
157
7.2.
The
Mathieu
group M12
161
7.3.
The
Mathieu
group
M
22 165
7.4.
The
Mathieu
group M23
172
7.5.
The
Mathieu
group M24
178
7.6.
The
Janko
group J\
180
7.7.
The
Janko
group J2
181
7.8.
The
Janko
group
Ą
183
7.9.
The
Janko
group J4
187
7.10.
The Higman-Sims group
HS 190
7.11.
The McLaughlin group McL
194
7.12.
The Suzuki group
5'иг
197
7.13.
The Conway group Co.-j
200
7.14.
The Conway group Co2
203
7.15.
The Conway group Co\
206
7.16.
The Fischer group Fi22
208
7.17.
The Fischer group Fi2z
211
7.18.
The Fischer group Fi'2i
215
7.19.
The Haiada-Norton group HN
=
F5
222
7.20.
The Thompson group Th
=
F3
224
7.21.
The Baby Monster
В
=
F2
226
7.22.
The Fischer-Griess Monster
M
=
Fi
229
7.23.
The Held group He
231
7.24.
The Rudvalis group Ru
233
7.25.
The O'Nan group
О 'Л'
237
7.26.
The Lyons group Ly
242
Chapter
8.
Details of proofs for individual groups
247
8.1.
Details for Mi2
247
8.2.
Details for J:}
249
CONTENTS
8.3.
Details
for
HS
8.4.
Details
for
Fi22
8.5.
Details
for
FÏ24.
8.6.
Details
for
ΗΝ
8.7.
Details
for
Ru
8.8.
Details
for
Ο'Ν
Bibliography
Index
250
253
255
264
265
272
275
281 |
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| id | DE-604.BV023481428 |
| illustrated | Not Illustrated |
| index_date | 2024-07-02T21:38:05Z |
| indexdate | 2024-07-09T21:19:45Z |
| institution | BVB |
| isbn | 9780821844748 |
| language | English |
| lccn | 2007060587 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016663551 |
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| physical | xvi, 289 Seiten Diagramme |
| publishDate | 2008 |
| publishDateSearch | 2008 |
| publishDateSort | 2008 |
| publisher | American Mathematical Society |
| record_format | marc |
| series | Mathematical surveys and monographs |
| series2 | Mathematical surveys and monographs |
| spelling | Benson, David J. 1955- Verfasser (DE-588)110324714 aut Classifying spaces of sporadic groups David J. Benson, Stephen D. Smith Providence, Rhode Island American Mathematical Society [2008] © 2008 xvi, 289 Seiten Diagramme txt rdacontent n rdamedia nc rdacarrier Mathematical surveys and monographs Volume 147 Sporadic groups (Mathematics) Classifying spaces Sporadische Gruppe (DE-588)4389412-4 gnd rswk-swf Klassifizierender Raum (DE-588)4164035-4 gnd rswk-swf Sporadische Gruppe (DE-588)4389412-4 s Klassifizierender Raum (DE-588)4164035-4 s DE-604 Smith, Stephen D. 1948- Verfasser (DE-588)1132740126 aut Erscheint auch als Online-Ausgabe 978-1-4704-1374-3 Mathematical surveys and monographs Volume 147 (DE-604)BV000018014 147 Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016663551&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Benson, David J. 1955- Smith, Stephen D. 1948- Classifying spaces of sporadic groups Mathematical surveys and monographs Sporadic groups (Mathematics) Classifying spaces Sporadische Gruppe (DE-588)4389412-4 gnd Klassifizierender Raum (DE-588)4164035-4 gnd |
| subject_GND | (DE-588)4389412-4 (DE-588)4164035-4 |
| title | Classifying spaces of sporadic groups |
| title_auth | Classifying spaces of sporadic groups |
| title_exact_search | Classifying spaces of sporadic groups |
| title_exact_search_txtP | Classifying spaces of sporadic groups |
| title_full | Classifying spaces of sporadic groups David J. Benson, Stephen D. Smith |
| title_fullStr | Classifying spaces of sporadic groups David J. Benson, Stephen D. Smith |
| title_full_unstemmed | Classifying spaces of sporadic groups David J. Benson, Stephen D. Smith |
| title_short | Classifying spaces of sporadic groups |
| title_sort | classifying spaces of sporadic groups |
| topic | Sporadic groups (Mathematics) Classifying spaces Sporadische Gruppe (DE-588)4389412-4 gnd Klassifizierender Raum (DE-588)4164035-4 gnd |
| topic_facet | Sporadic groups (Mathematics) Classifying spaces Sporadische Gruppe Klassifizierender Raum |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016663551&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000018014 |
| work_keys_str_mv | AT bensondavidj classifyingspacesofsporadicgroups AT smithstephend classifyingspacesofsporadicgroups |