Trees:
Saved in:
| Main Author: | |
|---|---|
| Other Authors: | |
| Format: | Book |
| Language: | English French |
| Published: |
Berlin ; Heidelberg ; New York ; Hong Kong ; London ; Milan ; Paris ; Tokyo
Springer
2003
|
| Edition: | Corrected second printing 2003 of the first english edition of 1980 |
| Series: | Springer monographs in mathematics
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | IX, 142 Seiten Diagramme |
| ISBN: | 9783540442370 3540442375 |
Staff View
MARC
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| 100 | 1 | |a Serre, Jean-Pierre |d 1926- |0 (DE-588)142283126 |4 aut | |
| 240 | 1 | 0 | |a Arbres, Amalgames, SL 2. Astérisque no.4. (1977) |
| 245 | 1 | 0 | |a Trees |c Jean-Pierre Serre ; translated from the French by John Stillwell |
| 250 | |a Corrected second printing 2003 of the first english edition of 1980 | ||
| 264 | 1 | |a Berlin ; Heidelberg ; New York ; Hong Kong ; London ; Milan ; Paris ; Tokyo |b Springer |c 2003 | |
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| 650 | 4 | |a Groupes linéaires algébriques | |
| 650 | 4 | |a Free groups | |
| 650 | 4 | |a Linear algebraic groups | |
| 650 | 4 | |a Trees (Graph theory) | |
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Record in the Search Index
| _version_ | 1811275017693954048 |
|---|---|
| adam_text |
Table
of
Contents
Introduction
.
VII
Chapter I. Trees and Amalgams
. 1
§1
Amalgams
. 1
1.1
Direct limits
. 1
1.2
Structure of amalgams
. 2
1.3
Consequences of the structure theorem
. 5
1.4
Constructions using amalgams
. 8
1.5
Examples
. 11
§2
Trees
. 13
2.1
Graphs
. 13
2.2
Trees
. 17
2.3
Subtrees of a graph
. 21
§3
Trees and free groups
. 25
3.1
Trees of representatives
. 25
3.2
Graph of a free group
. 26
3.3
Free actions on a tree
. 27
3.4
Application: Schreier's theorem
. 29
Appendix
:
Presentation of a group of homeomorphisms
30
§4
Trees and amalgams
. 32
4.1
The case of two factors
. 32
4.2
Examples of trees associated with amalgams
. 35
4.3
Applications
. 36
4.4
Limit of a tree of groups
. 37
4.5
Amalgams and fundamental domains (general case)
38
§5
Structure of a group acting on a tree
. 41
5.1
Fundamental group of a graph of groups
. 41
5.2
Reduced words
. 45
5.3
Universal covering relative to a graph of groups
. . 50
5.4
Structure theorem
. 54
5.5
Application: Kurosh's theorem
. 56
§6
Amalgams and fixed points
. 58
6.1
The fixed point property for groups acting on trees
58
6.2
Consequences of property (FA)
. 59
Vr Table
of Contents
6.3
Examples
. 60
6.4
Fixed points of an automorphism of a tree
. 61
6.5
Groups with fixed points (auxiliary results)
. 64
6.6
The case of SL3(Z)
. 67
Chapter II. SL2
. 69
§1
The tree of SL2 over a local field
. 69
1.1
The tree
. 69
1.2
The groups
GL(F)
and SL(F)
. 74
1.3
Action of GL(F) on the tree of V; stabilizers
. 76
1.4
Amalgams
. 78
1.5
Ihara's theorem
. 82
1.6
Nagao's theorem
. 85
1.7
Connection with Tits systems
. 89
§2
Arithmetic subgroups of the groups GL2 and SL2 over a
function field of one variable
. 96
2.1
Interpretation of the vertices of
Г\Х
as classes of
vector bundles of rank
2
over
С
. 96
2.2
Bundles of rank
1
and decomposable bundles
. 99
2.3
Structure of
Г\Х
. 103
2.4
Examples
.
Ill
2.5
Structure of
Г
. 117
2.6
Auxiliary results
. 120
2.7
Structure of
Г
:
case of a finite field
. 124
2.8
Homology
. 125
2.9
Euler-Poincaré
characteristic
. 131
Bibliography
. 137
Index
. 141 |
| any_adam_object | 1 |
| author | Serre, Jean-Pierre 1926- |
| author2 | Stillwell, John 1942- |
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| author_facet | Serre, Jean-Pierre 1926- Stillwell, John 1942- |
| author_role | aut |
| author_sort | Serre, Jean-Pierre 1926- |
| author_variant | j p s jps |
| building | Verbundindex |
| bvnumber | BV016463336 |
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| dewey-full | 511/.52 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 511 - General principles of mathematics |
| dewey-raw | 511/.52 |
| dewey-search | 511/.52 |
| dewey-sort | 3511 252 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | Corrected second printing 2003 of the first english edition of 1980 |
| format | Book |
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| id | DE-604.BV016463336 |
| illustrated | Not Illustrated |
| indexdate | 2024-09-26T16:01:04Z |
| institution | BVB |
| isbn | 9783540442370 3540442375 |
| language | English French |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-010178369 |
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| physical | IX, 142 Seiten Diagramme |
| publishDate | 2003 |
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| publisher | Springer |
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| series2 | Springer monographs in mathematics |
| spelling | Serre, Jean-Pierre 1926- (DE-588)142283126 aut Arbres, Amalgames, SL 2. Astérisque no.4. (1977) Trees Jean-Pierre Serre ; translated from the French by John Stillwell Corrected second printing 2003 of the first english edition of 1980 Berlin ; Heidelberg ; New York ; Hong Kong ; London ; Milan ; Paris ; Tokyo Springer 2003 IX, 142 Seiten Diagramme txt rdacontent n rdamedia nc rdacarrier Springer monographs in mathematics Arbres (Théorie des graphes) Groupes de Lie semi-simples Groupes libres Groupes linéaires algébriques Free groups Linear algebraic groups Trees (Graph theory) Amalgam Gruppentheorie (DE-588)4272864-2 gnd rswk-swf Baum Mathematik (DE-588)4004849-4 gnd rswk-swf Lineare Gruppe (DE-588)4138778-8 gnd rswk-swf Lineare Gruppe (DE-588)4138778-8 s Amalgam Gruppentheorie (DE-588)4272864-2 s Baum Mathematik (DE-588)4004849-4 s DE-604 Stillwell, John 1942- (DE-588)128427264 trl Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010178369&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Serre, Jean-Pierre 1926- Trees Arbres (Théorie des graphes) Groupes de Lie semi-simples Groupes libres Groupes linéaires algébriques Free groups Linear algebraic groups Trees (Graph theory) Amalgam Gruppentheorie (DE-588)4272864-2 gnd Baum Mathematik (DE-588)4004849-4 gnd Lineare Gruppe (DE-588)4138778-8 gnd |
| subject_GND | (DE-588)4272864-2 (DE-588)4004849-4 (DE-588)4138778-8 |
| title | Trees |
| title_alt | Arbres, Amalgames, SL 2. Astérisque no.4. (1977) |
| title_auth | Trees |
| title_exact_search | Trees |
| title_full | Trees Jean-Pierre Serre ; translated from the French by John Stillwell |
| title_fullStr | Trees Jean-Pierre Serre ; translated from the French by John Stillwell |
| title_full_unstemmed | Trees Jean-Pierre Serre ; translated from the French by John Stillwell |
| title_short | Trees |
| title_sort | trees |
| topic | Arbres (Théorie des graphes) Groupes de Lie semi-simples Groupes libres Groupes linéaires algébriques Free groups Linear algebraic groups Trees (Graph theory) Amalgam Gruppentheorie (DE-588)4272864-2 gnd Baum Mathematik (DE-588)4004849-4 gnd Lineare Gruppe (DE-588)4138778-8 gnd |
| topic_facet | Arbres (Théorie des graphes) Groupes de Lie semi-simples Groupes libres Groupes linéaires algébriques Free groups Linear algebraic groups Trees (Graph theory) Amalgam Gruppentheorie Baum Mathematik Lineare Gruppe |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010178369&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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