A course on geometric group theory:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Tokyo
MSJ
2006
|
| Series: | MSJ memoirs
16 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | X, 104 S. graph. Darst. |
| ISBN: | 4931469353 |
Staff View
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Record in the Search Index
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| adam_text | A COURSE ON GEOMETRIC GROUP THEORY BRIAN H. BOWDITCH 111 CONTENTS. 0.
INDRODUCTION 1 1. GROUP PRESENTATIONS 2 1.1. NOTATION 2 1.2. GENERATING
SETS 2 1.3. FREE GROUPS 5 1.4. CONSTRUCTION OF FREE GROUPS 7 1.5. GROUP
PRESENTATIONS 10 1.6. ABELIANISATIONS 12 2. CAYLEY GRAPHS 13 2.1. BASIC
TERMINOLOGY AND NOTATION 13 2.2. GRAPHS VIEWED AS METRIC AND TOPOLOGICAL
SPACES 14 2.3. GRAPHS ASSOCIATED TO GROUPS 15 3. QUASI-ISOMETRIES 22
3.1. METRIC SPACES 22 3.2. ISOMETRIES 25 3.3. DEFINITION OF
QUASI-ISOMETRIES 26 3.4. CAYLEY GRAPHS AGAIN 32 3.5. A USEFUL
CONSTRUCTION 34 3.6. QUASI-ISOMETRY AND COMMENSURABILITY 35 3.7.
QUASI-ISOMETRY INVARIANTS 39 4. FUNDAMENTAL GROUPS 40 4.1. DEFINITION OF
FUNDAMENTAL GROUPS 40 4.2. COVERING SPACES 44 4.3. APPLICATIONS TO FREE
GROUPS 46 IX 5. HYPERBOLIC GEOMETRY 49 5.1. THE HYPERBOLIC PLANE 49 5.2.
SOME PROPERTIES OF THE HYPERBOLIC PLANE 52 5.3. TESSELLATIONS OF H 2 53
5.4. SURFACES 54 5.5. 3-DIMENSIONAL HYPERBOLIC GEOMETRY 58 6. HYPERBOLIC
GROUPS 61 6.1. DEFINITION OF A HYPERBOLIC SPACE 61 6.2. BASIC PROPERTIES
63 6.3. PROJECTIONS 67 6.4. TREES IN HYPERBOLIC SPACES 69 6.5. THE
FOUR-POINT CONDITION 72 6.6. EXPONENTIAL GROWTH OF DISTANCES 75 6.7.
QUASIGEODESICS 77 6.8. HAUSDORFF DISTANCES 80 6.9. QUASI-ISOMETRY
INVARIANCE OF HYPERBOLICITY 80 6.10. HYPERBOLIC GROUPS 82 6.11. SOME
PROPERTIES OF HYPERBOLIC GROUPS 83 7. NOTES 89 REFERENCES 95
|
| adam_txt |
A COURSE ON GEOMETRIC GROUP THEORY BRIAN H. BOWDITCH 111 CONTENTS. 0.
INDRODUCTION 1 1. GROUP PRESENTATIONS 2 1.1. NOTATION 2 1.2. GENERATING
SETS 2 1.3. FREE GROUPS 5 1.4. CONSTRUCTION OF FREE GROUPS 7 1.5. GROUP
PRESENTATIONS 10 1.6. ABELIANISATIONS 12 2. CAYLEY GRAPHS 13 2.1. BASIC
TERMINOLOGY AND NOTATION 13 2.2. GRAPHS VIEWED AS METRIC AND TOPOLOGICAL
SPACES 14 2.3. GRAPHS ASSOCIATED TO GROUPS 15 3. QUASI-ISOMETRIES 22
3.1. METRIC SPACES 22 3.2. ISOMETRIES 25 3.3. DEFINITION OF
QUASI-ISOMETRIES 26 3.4. CAYLEY GRAPHS AGAIN 32 3.5. A USEFUL
CONSTRUCTION 34 3.6. QUASI-ISOMETRY AND COMMENSURABILITY 35 3.7.
QUASI-ISOMETRY INVARIANTS 39 4. FUNDAMENTAL GROUPS 40 4.1. DEFINITION OF
FUNDAMENTAL GROUPS 40 4.2. COVERING SPACES 44 4.3. APPLICATIONS TO FREE
GROUPS 46 IX 5. HYPERBOLIC GEOMETRY 49 5.1. THE HYPERBOLIC PLANE 49 5.2.
SOME PROPERTIES OF THE HYPERBOLIC PLANE 52 5.3. TESSELLATIONS OF H 2 53
5.4. SURFACES 54 5.5. 3-DIMENSIONAL HYPERBOLIC GEOMETRY 58 6. HYPERBOLIC
GROUPS 61 6.1. DEFINITION OF A HYPERBOLIC SPACE 61 6.2. BASIC PROPERTIES
63 6.3. PROJECTIONS 67 6.4. TREES IN HYPERBOLIC SPACES 69 6.5. THE
FOUR-POINT CONDITION 72 6.6. EXPONENTIAL GROWTH OF DISTANCES 75 6.7.
QUASIGEODESICS 77 6.8. HAUSDORFF DISTANCES 80 6.9. QUASI-ISOMETRY
INVARIANCE OF HYPERBOLICITY 80 6.10. HYPERBOLIC GROUPS 82 6.11. SOME
PROPERTIES OF HYPERBOLIC GROUPS 83 7. NOTES 89 REFERENCES 95 |
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| id | DE-604.BV023395876 |
| illustrated | Illustrated |
| index_date | 2024-07-02T21:21:47Z |
| indexdate | 2024-07-09T21:17:40Z |
| institution | BVB |
| isbn | 4931469353 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016578743 |
| oclc_num | 76741720 |
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| physical | X, 104 S. graph. Darst. |
| publishDate | 2006 |
| publishDateSearch | 2006 |
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| publisher | MSJ |
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| series | MSJ memoirs |
| series2 | MSJ memoirs |
| spelling | Bowditch, Brian H. 1961- Verfasser (DE-588)142346187 aut A course on geometric group theory Brian H. Bowditch Tokyo MSJ 2006 X, 104 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier MSJ memoirs 16 Geometric group theory Hyperbolic groups Geometrische Gruppentheorie (DE-588)4651615-3 gnd rswk-swf Geometrische Gruppentheorie (DE-588)4651615-3 s DE-604 MSJ memoirs 16 (DE-604)BV013976406 16 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016578743&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Bowditch, Brian H. 1961- A course on geometric group theory MSJ memoirs Geometric group theory Hyperbolic groups Geometrische Gruppentheorie (DE-588)4651615-3 gnd |
| subject_GND | (DE-588)4651615-3 |
| title | A course on geometric group theory |
| title_auth | A course on geometric group theory |
| title_exact_search | A course on geometric group theory |
| title_exact_search_txtP | A course on geometric group theory |
| title_full | A course on geometric group theory Brian H. Bowditch |
| title_fullStr | A course on geometric group theory Brian H. Bowditch |
| title_full_unstemmed | A course on geometric group theory Brian H. Bowditch |
| title_short | A course on geometric group theory |
| title_sort | a course on geometric group theory |
| topic | Geometric group theory Hyperbolic groups Geometrische Gruppentheorie (DE-588)4651615-3 gnd |
| topic_facet | Geometric group theory Hyperbolic groups Geometrische Gruppentheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016578743&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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