Groups, graphs and trees: an introduction to the geometry of infinite groups
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cambridge [u.a.]
Cambridge University Press
[2008]
|
| Edition: | first published |
| Series: | London Mathematical Society student texts
73 |
| Subjects: | |
| Online Access: | Contributor biographical information Publisher description Table of contents only Inhaltsverzeichnis |
| Item Description: | Includes bibliographical references and index |
| Physical Description: | xi, 231 Seiten Illustrationen |
| ISBN: | 9780521895453 9780521719773 |
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MARC
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| 100 | 1 | |a Meier, John |d 1965- |0 (DE-588)136391141 |4 aut | |
| 245 | 1 | 0 | |a Groups, graphs and trees |b an introduction to the geometry of infinite groups |c John Meier |
| 250 | |a first published | ||
| 264 | 1 | |a Cambridge [u.a.] |b Cambridge University Press |c [2008] | |
| 264 | 4 | |c © 2008 | |
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| 490 | 1 | |a London Mathematical Society student texts |v 73 | |
| 500 | |a Includes bibliographical references and index | ||
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Record in the Search Index
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| adam_text |
Contents
Preface
page
ix
1
Cayley's Theorems
1
1.1
Cayley's Basic Theorem
1
1.2
Graphs
6
1.3
Symmetry Groups of Graphs
10
1.4
Orbits and Stabilizers
15
1.5
Generating Sets and Cayley Graphs
17
1.6
More Cayley Graphs
22
1.7
Symmetries of Cayley Graphs
29
1.8
Fundamental Domains and Generating Sets
30
1.9
Words and Paths
37
2
Groups Generated by Reflections
44
3
Groups Acting on Trees
54
3.1
Free Groups
54
3.2
F3 is a Subgroup of F2
65
3.3
Free Group Homomorphisms and
Group Presentations
67
3.4
Pree
Groups and Actions on Trees
70
3.5
The Group Z3
*
Z4
73
3.6
FVee Products of Groups
79
3.7
Free Products of Finite Groups are Virtually Free
83
3.8
A Geometric View of Theorem
3.35 87
3.9
Finite Groups Acting on Trees
89
3.10
Serre's Property FA and Infinite Groups
90
4
Baumslag-Solitar Groups
100
vii
viii Contents
5
Words and Dehn's Word Problem
105
5.1
Normal Forms
105
5.2
Dehn's Word Problem
109
5.3
The Word Problem and Cay ley Graphs
111
5.4
The Cayley Graph of BS(1,2)
115
6
A Finitely Generated, Infinite Torsion Group
120
7
Regular Languages and Normal Forms
130
7.1
Regular Languages and Automata
130
7.2
Not All Languages are Regular
136
7.3
Regular Word Problem?
140
7.4
A Return to Normal Forms
141
7.5
Finitely Generated Subgroups of Free Groups
143
8
The Lamplighter Group
151
9
The Geometry of Infinite Groups
162
9.1
Gromov's Corollary, aka The Word Metric
162
9.2
The Growth of Groups, I
168
9.3
Growth and Regular Languages
172
9.4
Cannon Pairs
175
9.5
Cannon's Almost Convexity
179
10
Thompson's Group
187
11
The Large-Scale Geometry of Groups
198
11.1
Changing Generators
198
11.2
The Growth of Groups, II
202
11.3
The Growth of Thompson's Group
205
11.4
The Ends of Groups
208
11.5
The Freudenthai-Hopf Theorem
211
11.6
Two-Ended Groups
212
11.7
Commensurable Groups and Quasi-Isometry
217
Bibliography
227
Index
230 |
| adam_txt |
Contents
Preface
page
ix
1
Cayley's Theorems
1
1.1
Cayley's Basic Theorem
1
1.2
Graphs
6
1.3
Symmetry Groups of Graphs
10
1.4
Orbits and Stabilizers
15
1.5
Generating Sets and Cayley Graphs
17
1.6
More Cayley Graphs
22
1.7
Symmetries of Cayley Graphs
29
1.8
Fundamental Domains and Generating Sets
30
1.9
Words and Paths
37
2
Groups Generated by Reflections
44
3
Groups Acting on Trees
54
3.1
Free Groups
54
3.2
F3 is a Subgroup of F2
65
3.3
Free Group Homomorphisms and
Group Presentations
67
3.4
Pree
Groups and Actions on Trees
70
3.5
The Group Z3
*
Z4
73
3.6
FVee Products of Groups
79
3.7
Free Products of Finite Groups are Virtually Free
83
3.8
A Geometric View of Theorem
3.35 87
3.9
Finite Groups Acting on Trees
89
3.10
Serre's Property FA and Infinite Groups
90
4
Baumslag-Solitar Groups
100
vii
viii Contents
5
Words and Dehn's Word Problem
105
5.1
Normal Forms
105
5.2
Dehn's Word Problem
109
5.3
The Word Problem and Cay ley Graphs
111
5.4
The Cayley Graph of BS(1,2)
115
6
A Finitely Generated, Infinite Torsion Group
120
7
Regular Languages and Normal Forms
130
7.1
Regular Languages and Automata
130
7.2
Not All Languages are Regular
136
7.3
Regular Word Problem?
140
7.4
A Return to Normal Forms
141
7.5
Finitely Generated Subgroups of Free Groups
143
8
The Lamplighter Group
151
9
The Geometry of Infinite Groups
162
9.1
Gromov's Corollary, aka The Word Metric
162
9.2
The Growth of Groups, I
168
9.3
Growth and Regular Languages
172
9.4
Cannon Pairs
175
9.5
Cannon's Almost Convexity
179
10
Thompson's Group
187
11
The Large-Scale Geometry of Groups
198
11.1
Changing Generators
198
11.2
The Growth of Groups, II
202
11.3
The Growth of Thompson's Group
205
11.4
The Ends of Groups
208
11.5
The Freudenthai-Hopf Theorem
211
11.6
Two-Ended Groups
212
11.7
Commensurable Groups and Quasi-Isometry
217
Bibliography
227
Index
230 |
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| index_date | 2024-07-02T21:46:57Z |
| indexdate | 2024-10-31T15:00:32Z |
| institution | BVB |
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| language | English |
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| spelling | Meier, John 1965- (DE-588)136391141 aut Groups, graphs and trees an introduction to the geometry of infinite groups John Meier first published Cambridge [u.a.] Cambridge University Press [2008] © 2008 xi, 231 Seiten Illustrationen txt rdacontent n rdamedia nc rdacarrier London Mathematical Society student texts 73 Includes bibliographical references and index Infinite groups Unendliche Gruppe (DE-588)4375539-2 gnd rswk-swf Unendliche Gruppe (DE-588)4375539-2 s DE-604 London Mathematical Society student texts 73 (DE-604)BV000841726 73 http://www.loc.gov/catdir/enhancements/fy0827/2008012848-b.html Contributor biographical information http://www.loc.gov/catdir/enhancements/fy0827/2008012848-d.html Publisher description http://www.loc.gov/catdir/enhancements/fy0827/2008012848-t.html Table of contents only Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016692043&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Meier, John 1965- Groups, graphs and trees an introduction to the geometry of infinite groups London Mathematical Society student texts Infinite groups Unendliche Gruppe (DE-588)4375539-2 gnd |
| subject_GND | (DE-588)4375539-2 |
| title | Groups, graphs and trees an introduction to the geometry of infinite groups |
| title_auth | Groups, graphs and trees an introduction to the geometry of infinite groups |
| title_exact_search | Groups, graphs and trees an introduction to the geometry of infinite groups |
| title_exact_search_txtP | Groups, graphs and trees an introduction to the geometry of infinite groups |
| title_full | Groups, graphs and trees an introduction to the geometry of infinite groups John Meier |
| title_fullStr | Groups, graphs and trees an introduction to the geometry of infinite groups John Meier |
| title_full_unstemmed | Groups, graphs and trees an introduction to the geometry of infinite groups John Meier |
| title_short | Groups, graphs and trees |
| title_sort | groups graphs and trees an introduction to the geometry of infinite groups |
| title_sub | an introduction to the geometry of infinite groups |
| topic | Infinite groups Unendliche Gruppe (DE-588)4375539-2 gnd |
| topic_facet | Infinite groups Unendliche Gruppe |
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