Tree lattices:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Boston [u.a.]
Birkhäuser
2001
|
| Series: | Progress in mathematics
176 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XII, 233 S. Ill., graph. Darst. |
| ISBN: | 3764341203 0817641203 |
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MARC
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Record in the Search Index
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|---|---|
| adam_text | Contents
Preface xi
0 Introduction 1
0.1 Tree lattices 1
0.2 X lattices and H lattices 2
0.3 Near simplicity 3
0.4 The structure of tree lattices 4
0.5 Existence of lattices 4
0.6 The structure of A = F X 6
0.7 Volumes 7
0.8 Centralizers, normalizers, commensurators 8
1 Lattices and Volumes 13
1.1 Haar measure 13
1.2 Lattices and unimodularity 13
1.3 Compact open subgroups 13
1.5 Discrete group covolumes 14
2 Graphs of Groups and Edge Indexed Graphs 17
2.1 Graphs 17
2.2 Morphisms and actions 18
2.3 Graphs of groups 18
2.4 Quotient graphs of groups 19
2.5 Edge indexed graphs and their groupings 19
2.6 Unimodularity, volumes, bounded denominators 20
3 Tree Lattices 25
3.1 Topology on G = AutX 25
3.2 Tree lattices 25
3.3 The group G//of deck transformations 26
3.5 Discreteness Criterion; Rigidity of (A, i) 27
3.6 Unimodularity and volume 29
3.8 Existence of tree lattices 30
3.12 The structure of tree lattices 31
3.14 Non arithmetic uniform commensurators 33
4 Arbitrary Real Volumes, Cusps, and Homology 35
4.0 Introduction 35
4.1 Grafting 36
4.2 Volumes 38
4.8 Cusps 43
4.9 Geometric parabolic ends 44
4.10 F parabolic ends and F cusps 49
4.11 Unidirectional examples 51
4.12 A planar example 54
5 Length Functions, Minimality 67
5.1 Hyperbolic length (cf. [B3], II, §6) 67
5.4 Minimality 68
5.14 Abelian actions 71
5.15 Non abelian actions 71
5.16 Abelian discrete actions 71
6 Centralizers, Normalizers, and Commensurators 73
6.0 Introduction 73
6.1 Notation 74
6.6 Non minimal centralizers 77
6.9 NIF, for minimal non abelian actions 80
6.10 Some normal subgroups 81
6.11 The Tits Independence Condition 82
6.13 Remarks 85
6.16 Automorphism groups of rooted trees 86
6.17 Automorphism groups of ended trees 88
6.21 Remarks 90
7 Existence of Tree Lattices 91
7.1 Introduction 91
7.2 Open fanning 93
7.5 Multiple open fanning 98
8 Non Uniform Lattices on Uniform Trees 103
8.1 Carbone s Theorem 103
8.6 Proof of Theorem (8.2) 110
8.7 Remarks 110
8.8 Examples. Loops and cages Ill
8.9 Two vertex graphs 116
9 Parabolic Actions, Lattices, and Trees 119
9.0 Introduction 119
9.1 Ends(X) 120
9.2 Horospheres and horoballs 121
9.3 End stabilizers 122
9.4 Parabolic actions 123
9.5 Parabolic trees 125
9.6 Parabolic lattices 125
9.8 Restriction to horoballs 126
9.9 Parabolic lattices with linear quotient 127
9.10 Parabolic ray lattices 131
9.13 Parabolic lattices with all horospheres infinite 139
9.14 A bounded degree example 143
9.15 Tree lattices that are simple groups must be parabolic 148
9.16 Lattices on a product of two trees 149
10 Lattices of Nagao Type 151
10.1 Nagao rays 151
10.2 Nagao sTheorem: V = PGL2(Fq[t]) 157
10.3 A divisible (q + l) regular grouping 160
10.4 The PNeumann groupings 161
10.5 The symmetric groupings 163
10.6 Product groupings 164
Appendix [BCR]: The Existence Theorem for Tree Lattices
Hyman Bass, Lisa Carbone, and Gabriel Rosenberg 167
Appendix [BT]: Discreteness Criteria for Tree Automorphism Groups
Hyman Bass and Jacques Tits 185
Appendix [PN]: The PNeumann Groups
Hyman Bass and Alexander Lubotzky 213
References 223
Index of Notation 229
Index 231
|
| any_adam_object | 1 |
| author | Bass, Hyman 1932- Lubotzky, Alexander |
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| ctrlnum | (OCoLC)44713371 (DE-599)BVBBV013334159 |
| 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 |
| format | Book |
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| id | DE-604.BV013334159 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T18:43:59Z |
| institution | BVB |
| isbn | 3764341203 0817641203 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009092590 |
| oclc_num | 44713371 |
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| owner | DE-355 DE-BY-UBR DE-20 DE-29T DE-703 DE-11 |
| owner_facet | DE-355 DE-BY-UBR DE-20 DE-29T DE-703 DE-11 |
| physical | XII, 233 S. Ill., graph. Darst. |
| publishDate | 2001 |
| publishDateSearch | 2001 |
| publishDateSort | 2001 |
| publisher | Birkhäuser |
| record_format | marc |
| series | Progress in mathematics |
| series2 | Progress in mathematics |
| spelling | Bass, Hyman 1932- Verfasser (DE-588)123540097 aut Tree lattices Hyman Bass ; Alexander Lubotzky Boston [u.a.] Birkhäuser 2001 XII, 233 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Progress in mathematics 176 Lie groups Trees (Graph theory) Lie-Gruppe (DE-588)4035695-4 gnd rswk-swf Graphentheorie (DE-588)4113782-6 gnd rswk-swf Baum Mathematik (DE-588)4004849-4 gnd rswk-swf Graphentheorie (DE-588)4113782-6 s DE-604 Baum Mathematik (DE-588)4004849-4 s Lie-Gruppe (DE-588)4035695-4 s Lubotzky, Alexander Verfasser aut Progress in mathematics 176 (DE-604)BV000004120 176 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009092590&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Bass, Hyman 1932- Lubotzky, Alexander Tree lattices Progress in mathematics Lie groups Trees (Graph theory) Lie-Gruppe (DE-588)4035695-4 gnd Graphentheorie (DE-588)4113782-6 gnd Baum Mathematik (DE-588)4004849-4 gnd |
| subject_GND | (DE-588)4035695-4 (DE-588)4113782-6 (DE-588)4004849-4 |
| title | Tree lattices |
| title_auth | Tree lattices |
| title_exact_search | Tree lattices |
| title_full | Tree lattices Hyman Bass ; Alexander Lubotzky |
| title_fullStr | Tree lattices Hyman Bass ; Alexander Lubotzky |
| title_full_unstemmed | Tree lattices Hyman Bass ; Alexander Lubotzky |
| title_short | Tree lattices |
| title_sort | tree lattices |
| topic | Lie groups Trees (Graph theory) Lie-Gruppe (DE-588)4035695-4 gnd Graphentheorie (DE-588)4113782-6 gnd Baum Mathematik (DE-588)4004849-4 gnd |
| topic_facet | Lie groups Trees (Graph theory) Lie-Gruppe Graphentheorie Baum Mathematik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009092590&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000004120 |
| work_keys_str_mv | AT basshyman treelattices AT lubotzkyalexander treelattices |