Cohomology of finite and affine type Artin groups over Abelian representation:
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| Main Author: | |
|---|---|
| Format: | Thesis Book |
| Language: | English |
| Published: |
Pisa
Edizioni della normale
2009
|
| Series: | Tesi
13 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | IX, 137 S. graph. Darst. |
| ISBN: | 9788876423451 |
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MARC
| LEADER | 00000nam a2200000 cb4500 | ||
|---|---|---|---|
| 001 | BV035674408 | ||
| 003 | DE-604 | ||
| 005 | 20180313 | ||
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| 008 | 090812s2009 d||| m||| 00||| eng d | ||
| 020 | |a 9788876423451 |9 978-88-7642-345-1 | ||
| 035 | |a (OCoLC)406122801 | ||
| 035 | |a (DE-599)BVBBV035674408 | ||
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| 100 | 1 | |a Callegaro, Filippo |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Cohomology of finite and affine type Artin groups over Abelian representation |c Filippo Callegaro |
| 264 | 1 | |a Pisa |b Edizioni della normale |c 2009 | |
| 300 | |a IX, 137 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Tesi |v 13 | |
| 502 | |a Pisa, Scuola Normale Superiore, tesi, 2007 | ||
| 650 | 4 | |a Artin algebras | |
| 650 | 4 | |a Cohomology operations | |
| 650 | 4 | |a Coxeter groups | |
| 650 | 0 | 7 | |a Kohomologie |0 (DE-588)4031700-6 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Zopfgruppe |0 (DE-588)4225944-7 |2 gnd |9 rswk-swf |
| 655 | 7 | |0 (DE-588)4113937-9 |a Hochschulschrift |2 gnd-content | |
| 689 | 0 | 0 | |a Kohomologie |0 (DE-588)4031700-6 |D s |
| 689 | 0 | 1 | |a Zopfgruppe |0 (DE-588)4225944-7 |D s |
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| 830 | 0 | |a Tesi |v 13 |w (DE-604)BV035447349 |9 13 | |
| 856 | 4 | 2 | |m Digitalisierung UB Regensburg |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017728632&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-017728632 | ||
Record in the Search Index
| _version_ | 1804139371815763968 |
|---|---|
| adam_text | Contents
Acknowledgments
xi
Introduction
xiii
1
Coxeter groups and arrangements
1
1.1.
Coxeter groups
...................... 1
1.2.
Coxeter groups and arrangements
............ 2
1.3.
Finite and
affine
Coxeter groups
............. 4
1.4.
Κ (π,
1)
spaces, arrangements and
Artin
groups
..... 7
1.5.
Poincaré
polynomials and
Poincaré
series
........ 14
1.6.
The Milnor fibration for arrangements
.......... 16
2
Group cohomology and local systems
21
2.1.
Principal bundles and
Κ (π,
1)
spaces
.......... 21
2.2.
Homology and cohomology of groups
.......... 22
2.3.
Cohomology of
Artin
groups
............... 25
2.4.
Fibrations for
Artin
groups
................ 28
2.5.
A topological construction
................ 29
2.6.
The Shapiro s Lemma
................... 30
2.7.
Topology of the Milnor fiber for
Artin
groups
...... 31
2.8.
Cohomology of the Milnor fiber
............. 33
3
Topology of arrangements
35
3.1.
The Salvetti complex
................... 35
3.2.
Filtrations on the Salvetti complex: an example
..... 41
3.3.
Filtrations and spectral sequences
............ 43
3.4.
The Novikov homology and degree shift
......... 44
3.5.
Well filtered complexes and degree shift
......... 48
3.5.1.
Main theorem
................... 48
3.5.2.
Applications
................... 53
viii
Filippo Callegaro
4
The integral
homology of the Milnor fiber for Artin groups
of type
A„ 55
4.1.
Notations and definitions
................. 55
4.2.
The Milnor
fiber and some lemmas............
57
4.3.
Computations and results
................. 61
4.4.
Main Result
........................ 68
5
The integral homology of the Milnor fiber for Artin groups
of type Bn
73
5.1.
Filtration and spectral sequence for Bn
.......... 73
5.2.
Computations
....................... 75
Case
ρ
= 0,
m =
2.................... 78
Case
ρ =
0,
m
> 2, 2
| m
................. 78
Case p = 2,m = 2
.................... 78
Case
ρ
= 2,
m
> 2,2
m
................. 79
Case
ρ
> 2,
m
= 2.................... 79
Case p>2,m>2,2 m,p m
............. 80
Bockstein homomorphism................ 81
5.3. Main Theorem ...................... 83
6
The case of the
affine arrangements
of
type
A„ 85
6.1.
Introduction
........................ 85
6.2.
Inclusions
of
Artin
groups
................ 86
6.3.
The cohomology of
Gß„ ................. 88
6.3.1.
Proof of the
Main Theorem............ 88
6.3.2.
Other computations
................ 97
6.4.
More consequences
.................... 97
6.4.1.
Cohomology of
GĂn
_}
.............. 98
6.4.2.
Cohomology of GAn with coefficient
in the
Tong-
Yang
-Ма
representation
....... 99
7
The case of the
affine
arrangements of type Bn
103
7.1.
Preliminary constructions
................. 103
7.2.
The
К (я,
1)
problem for the
affine
Artin group
of type Bn
......................... 104
7.3.
Cohomology
....................... 106
7.3.1.
Algebraic complexes for Artin groups
...... 108
7.3.2.
A generalized shift
................ 109
7.3.3.
A splitting of complexes
.............
Ill
7.3.4.
Cohomology of K*Dn
..............
Ill
7.3.5.
Spectral sequence for
G
¿ ............
117
ix
Cohomology
of
Artin
Groups over Abelian Representations
Open problems
122
References
125
Index
133
|
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| classification_rvk | SK 260 SK 320 |
| ctrlnum | (OCoLC)406122801 (DE-599)BVBBV035674408 |
| dewey-full | 512 |
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| dewey-ones | 512 - Algebra |
| dewey-raw | 512 |
| dewey-search | 512 |
| dewey-sort | 3512 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Thesis Book |
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| genre_facet | Hochschulschrift |
| id | DE-604.BV035674408 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T21:43:02Z |
| institution | BVB |
| isbn | 9788876423451 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-017728632 |
| oclc_num | 406122801 |
| open_access_boolean | |
| owner | DE-355 DE-BY-UBR DE-11 DE-703 |
| owner_facet | DE-355 DE-BY-UBR DE-11 DE-703 |
| physical | IX, 137 S. graph. Darst. |
| publishDate | 2009 |
| publishDateSearch | 2009 |
| publishDateSort | 2009 |
| publisher | Edizioni della normale |
| record_format | marc |
| series | Tesi |
| series2 | Tesi |
| spelling | Callegaro, Filippo Verfasser aut Cohomology of finite and affine type Artin groups over Abelian representation Filippo Callegaro Pisa Edizioni della normale 2009 IX, 137 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Tesi 13 Pisa, Scuola Normale Superiore, tesi, 2007 Artin algebras Cohomology operations Coxeter groups Kohomologie (DE-588)4031700-6 gnd rswk-swf Zopfgruppe (DE-588)4225944-7 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content Kohomologie (DE-588)4031700-6 s Zopfgruppe (DE-588)4225944-7 s DE-604 Tesi 13 (DE-604)BV035447349 13 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017728632&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Callegaro, Filippo Cohomology of finite and affine type Artin groups over Abelian representation Tesi Artin algebras Cohomology operations Coxeter groups Kohomologie (DE-588)4031700-6 gnd Zopfgruppe (DE-588)4225944-7 gnd |
| subject_GND | (DE-588)4031700-6 (DE-588)4225944-7 (DE-588)4113937-9 |
| title | Cohomology of finite and affine type Artin groups over Abelian representation |
| title_auth | Cohomology of finite and affine type Artin groups over Abelian representation |
| title_exact_search | Cohomology of finite and affine type Artin groups over Abelian representation |
| title_full | Cohomology of finite and affine type Artin groups over Abelian representation Filippo Callegaro |
| title_fullStr | Cohomology of finite and affine type Artin groups over Abelian representation Filippo Callegaro |
| title_full_unstemmed | Cohomology of finite and affine type Artin groups over Abelian representation Filippo Callegaro |
| title_short | Cohomology of finite and affine type Artin groups over Abelian representation |
| title_sort | cohomology of finite and affine type artin groups over abelian representation |
| topic | Artin algebras Cohomology operations Coxeter groups Kohomologie (DE-588)4031700-6 gnd Zopfgruppe (DE-588)4225944-7 gnd |
| topic_facet | Artin algebras Cohomology operations Coxeter groups Kohomologie Zopfgruppe Hochschulschrift |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017728632&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV035447349 |
| work_keys_str_mv | AT callegarofilippo cohomologyoffiniteandaffinetypeartingroupsoverabelianrepresentation |