Relatively hyperbolic groups: intrinsic geometry, algebraic properties, and algorithmic problems
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Providence, R.I.
American Mathematical Society
2006
|
| Series: | Memoirs of the American Mathematical Society
843 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | "Volume 179, number 843 (second of 5 numbers)." Includes bibliographical references |
| Physical Description: | VI, 100 S. graph. Darst. |
| ISBN: | 0821838210 |
Staff View
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| 245 | 1 | 0 | |a Relatively hyperbolic groups |b intrinsic geometry, algebraic properties, and algorithmic problems |c Denis V. Osin |
| 264 | 1 | |a Providence, R.I. |b American Mathematical Society |c 2006 | |
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| 490 | 1 | |a Memoirs of the American Mathematical Society |v 843 | |
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| 500 | |a Includes bibliographical references | ||
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Record in the Search Index
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| adam_text | Contents
Chapter 1. Introduction 1
1.1. Preliminary remarks 1
1.2. Main results 3
Chapter 2. Relative isoperimetric inequalities 9
2.1. Relative presentations and length functions 9
2.2. Geometry of van Kampen diagrams over relative presentations 11
2.3. Relative Dehn functions 18
2.4. Splitting Theorem for relatively finitely presented groups 25
2.5. Isoperimetric functions of Cayley graphs. 30
Chapter 3. Geometry of finitely generated relatively hyperbolic groups 35
3.1. Conventions and notation 35
3.2. Properties of quasi geodesics 36
3.3. Geodesic triangles in Cayley graphs 45
3.4. Symmetric geodesies 51
Chapter 4. Algebraic properties 61
4.1. Elements of finite order 61
4.2. Relatively quasi convex subgroups 63
4.3. Cyclic subgroups and translation numbers 70
Chapter 5. Algorithmic problems 77
5.1. The word and membership problems 77
5.2. The parabolicity problems 79
5.3. Algorithmic problems for hyperbolic elements 82
Open questions 89
Appendix. Equivalent definitions of relative hyperbolicity 91
Bibliography 97
V
|
| adam_txt |
Contents
Chapter 1. Introduction 1
1.1. Preliminary remarks 1
1.2. Main results 3
Chapter 2. Relative isoperimetric inequalities 9
2.1. Relative presentations and length functions 9
2.2. Geometry of van Kampen diagrams over relative presentations 11
2.3. Relative Dehn functions 18
2.4. Splitting Theorem for relatively finitely presented groups 25
2.5. Isoperimetric functions of Cayley graphs. 30
Chapter 3. Geometry of finitely generated relatively hyperbolic groups 35
3.1. Conventions and notation 35
3.2. Properties of quasi geodesics 36
3.3. Geodesic triangles in Cayley graphs 45
3.4. Symmetric geodesies 51
Chapter 4. Algebraic properties 61
4.1. Elements of finite order 61
4.2. Relatively quasi convex subgroups 63
4.3. Cyclic subgroups and translation numbers 70
Chapter 5. Algorithmic problems 77
5.1. The word and membership problems 77
5.2. The parabolicity problems 79
5.3. Algorithmic problems for hyperbolic elements 82
Open questions 89
Appendix. Equivalent definitions of relative hyperbolicity 91
Bibliography 97
V |
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| index_date | 2024-07-02T13:59:48Z |
| indexdate | 2024-07-09T20:35:40Z |
| institution | BVB |
| isbn | 0821838210 |
| language | English |
| lccn | 2005053663 |
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| physical | VI, 100 S. graph. Darst. |
| publishDate | 2006 |
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| publisher | American Mathematical Society |
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| series2 | Memoirs of the American Mathematical Society |
| spelling | Osin, Denis V. 1974- Verfasser (DE-588)173812384 aut Relatively hyperbolic groups intrinsic geometry, algebraic properties, and algorithmic problems Denis V. Osin Providence, R.I. American Mathematical Society 2006 VI, 100 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Memoirs of the American Mathematical Society 843 "Volume 179, number 843 (second of 5 numbers)." Includes bibliographical references Groepentheorie gtt Hyperboliciteit gtt Teoria dos grupos larpcal Álgebra larpcal Geometric group theory Hyperbolic groups Geometrische Gruppentheorie (DE-588)4651615-3 gnd rswk-swf Hyperbolische Gruppe (DE-588)4238166-6 gnd rswk-swf Geometrische Gruppentheorie (DE-588)4651615-3 s Hyperbolische Gruppe (DE-588)4238166-6 s b DE-604 Memoirs of the American Mathematical Society 843 (DE-604)BV008000141 843 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014644308&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Osin, Denis V. 1974- Relatively hyperbolic groups intrinsic geometry, algebraic properties, and algorithmic problems Memoirs of the American Mathematical Society Groepentheorie gtt Hyperboliciteit gtt Teoria dos grupos larpcal Álgebra larpcal Geometric group theory Hyperbolic groups Geometrische Gruppentheorie (DE-588)4651615-3 gnd Hyperbolische Gruppe (DE-588)4238166-6 gnd |
| subject_GND | (DE-588)4651615-3 (DE-588)4238166-6 |
| title | Relatively hyperbolic groups intrinsic geometry, algebraic properties, and algorithmic problems |
| title_auth | Relatively hyperbolic groups intrinsic geometry, algebraic properties, and algorithmic problems |
| title_exact_search | Relatively hyperbolic groups intrinsic geometry, algebraic properties, and algorithmic problems |
| title_exact_search_txtP | Relatively hyperbolic groups intrinsic geometry, algebraic properties, and algorithmic problems |
| title_full | Relatively hyperbolic groups intrinsic geometry, algebraic properties, and algorithmic problems Denis V. Osin |
| title_fullStr | Relatively hyperbolic groups intrinsic geometry, algebraic properties, and algorithmic problems Denis V. Osin |
| title_full_unstemmed | Relatively hyperbolic groups intrinsic geometry, algebraic properties, and algorithmic problems Denis V. Osin |
| title_short | Relatively hyperbolic groups |
| title_sort | relatively hyperbolic groups intrinsic geometry algebraic properties and algorithmic problems |
| title_sub | intrinsic geometry, algebraic properties, and algorithmic problems |
| topic | Groepentheorie gtt Hyperboliciteit gtt Teoria dos grupos larpcal Álgebra larpcal Geometric group theory Hyperbolic groups Geometrische Gruppentheorie (DE-588)4651615-3 gnd Hyperbolische Gruppe (DE-588)4238166-6 gnd |
| topic_facet | Groepentheorie Hyperboliciteit Teoria dos grupos Álgebra Geometric group theory Hyperbolic groups Geometrische Gruppentheorie Hyperbolische Gruppe |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014644308&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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| work_keys_str_mv | AT osindenisv relativelyhyperbolicgroupsintrinsicgeometryalgebraicpropertiesandalgorithmicproblems |