The Geometry of Discrete Groups:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
New York, NY
Springer New York
1983
|
| Schriftenreihe: | Graduate Texts in Mathematics
91 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | This text is intended to serve as an introduction to the geometry of the action of discrete groups of Mobius transformations. The subject matter has now been studied with changing points of emphasis for over a hundred years, the most recent developments being connected with the theory of 3-manifolds: see, for example, the papers of Poincare [77] and Thurston [101]. About 1940, the now well-known (but virtually unobtainable) Fenchel-Nielsen manuscript appeared. Sadly, the manuscript never appeared in print, and this more modest text attempts to display at least some of the beautiful geometrical ideas to be found in that manuscript, as well as some more recent material. The text has been written with the conviction that geometrical explanations are essential for a full understanding of the material and that however simple a matrix proof might seem, a geometric proof is almost certainly more profitable. Further, wherever possible, results should be stated in a form that is invariant under conjugation, thus making the intrinsic nature of the result more apparent. Despite the fact that the subject matter is concerned with groups of isometries of hyperbolic geometry, many publications rely on Euclidean estimates and geometry. However, the recent developments have again emphasized the need for hyperbolic geometry, and I have included a comprehensive chapter on analytical (not axiomatic) hyperbolic geometry. It is hoped that this chapter will serve as a "dictionary" offormulae in plane hyperbolic geometry and as such will be of interest and use in its own right |
| Beschreibung: | 1 Online-Ressource (XII, 340 p) |
| ISBN: | 9781461211464 9781461270225 |
| ISSN: | 0072-5285 |
| DOI: | 10.1007/978-1-4612-1146-4 |
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Datensatz im Suchindex
| _version_ | 1804153090792751104 |
|---|---|
| any_adam_object | |
| author | Beardon, Alan F. |
| author_facet | Beardon, Alan F. |
| author_role | aut |
| author_sort | Beardon, Alan F. |
| author_variant | a f b af afb |
| building | Verbundindex |
| bvnumber | BV042419766 |
| classification_tum | MAT 000 |
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| dewey-full | 512.2 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512.2 |
| dewey-search | 512.2 |
| dewey-sort | 3512.2 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-1-4612-1146-4 |
| format | Electronic eBook |
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| id | DE-604.BV042419766 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:05Z |
| institution | BVB |
| isbn | 9781461211464 9781461270225 |
| issn | 0072-5285 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027855183 |
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| publishDate | 1983 |
| publishDateSearch | 1983 |
| publishDateSort | 1983 |
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| series | Graduate Texts in Mathematics |
| series2 | Graduate Texts in Mathematics |
| spelling | Beardon, Alan F. Verfasser aut The Geometry of Discrete Groups by Alan F. Beardon New York, NY Springer New York 1983 1 Online-Ressource (XII, 340 p) txt rdacontent c rdamedia cr rdacarrier Graduate Texts in Mathematics 91 0072-5285 This text is intended to serve as an introduction to the geometry of the action of discrete groups of Mobius transformations. The subject matter has now been studied with changing points of emphasis for over a hundred years, the most recent developments being connected with the theory of 3-manifolds: see, for example, the papers of Poincare [77] and Thurston [101]. About 1940, the now well-known (but virtually unobtainable) Fenchel-Nielsen manuscript appeared. Sadly, the manuscript never appeared in print, and this more modest text attempts to display at least some of the beautiful geometrical ideas to be found in that manuscript, as well as some more recent material. The text has been written with the conviction that geometrical explanations are essential for a full understanding of the material and that however simple a matrix proof might seem, a geometric proof is almost certainly more profitable. Further, wherever possible, results should be stated in a form that is invariant under conjugation, thus making the intrinsic nature of the result more apparent. Despite the fact that the subject matter is concerned with groups of isometries of hyperbolic geometry, many publications rely on Euclidean estimates and geometry. However, the recent developments have again emphasized the need for hyperbolic geometry, and I have included a comprehensive chapter on analytical (not axiomatic) hyperbolic geometry. It is hoped that this chapter will serve as a "dictionary" offormulae in plane hyperbolic geometry and as such will be of interest and use in its own right Mathematics Group theory Group Theory and Generalizations Mathematik Geometrie (DE-588)4020236-7 gnd rswk-swf Lineare Transformation (DE-588)4167712-2 gnd rswk-swf Diskrete Gruppe (DE-588)4135541-6 gnd rswk-swf Gruppentheorie (DE-588)4072157-7 gnd rswk-swf Hyperbolische Geometrie (DE-588)4161041-6 gnd rswk-swf Lineare Transformation (DE-588)4167712-2 s Diskrete Gruppe (DE-588)4135541-6 s Hyperbolische Geometrie (DE-588)4161041-6 s 1\p DE-604 Geometrie (DE-588)4020236-7 s 2\p DE-604 Gruppentheorie (DE-588)4072157-7 s 3\p DE-604 Graduate Texts in Mathematics 91 (DE-604)BV035421258 91 https://doi.org/10.1007/978-1-4612-1146-4 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Beardon, Alan F. The Geometry of Discrete Groups Graduate Texts in Mathematics Mathematics Group theory Group Theory and Generalizations Mathematik Geometrie (DE-588)4020236-7 gnd Lineare Transformation (DE-588)4167712-2 gnd Diskrete Gruppe (DE-588)4135541-6 gnd Gruppentheorie (DE-588)4072157-7 gnd Hyperbolische Geometrie (DE-588)4161041-6 gnd |
| subject_GND | (DE-588)4020236-7 (DE-588)4167712-2 (DE-588)4135541-6 (DE-588)4072157-7 (DE-588)4161041-6 |
| title | The Geometry of Discrete Groups |
| title_auth | The Geometry of Discrete Groups |
| title_exact_search | The Geometry of Discrete Groups |
| title_full | The Geometry of Discrete Groups by Alan F. Beardon |
| title_fullStr | The Geometry of Discrete Groups by Alan F. Beardon |
| title_full_unstemmed | The Geometry of Discrete Groups by Alan F. Beardon |
| title_short | The Geometry of Discrete Groups |
| title_sort | the geometry of discrete groups |
| topic | Mathematics Group theory Group Theory and Generalizations Mathematik Geometrie (DE-588)4020236-7 gnd Lineare Transformation (DE-588)4167712-2 gnd Diskrete Gruppe (DE-588)4135541-6 gnd Gruppentheorie (DE-588)4072157-7 gnd Hyperbolische Geometrie (DE-588)4161041-6 gnd |
| topic_facet | Mathematics Group theory Group Theory and Generalizations Mathematik Geometrie Lineare Transformation Diskrete Gruppe Gruppentheorie Hyperbolische Geometrie |
| url | https://doi.org/10.1007/978-1-4612-1146-4 |
| volume_link | (DE-604)BV035421258 |
| work_keys_str_mv | AT beardonalanf thegeometryofdiscretegroups |