Lectures on Hyperbolic Geometry:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Berlin, Heidelberg
Springer Berlin Heidelberg
1992
|
| Schriftenreihe: | Universitext
|
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | In recent years hyperbolic geometry has been the object and the preparation for extensive study that has produced important and often amazing results and also opened up new questions. The book concerns the geometry of manifolds and in particular hyperbolic manifolds; its aim is to provide an exposition of some fundamental results, and to be as far as possible self-contained, complete, detailed and unified. Since it starts from the basics and it reaches recent developments of the theory, the book is mainly addressed to graduate-level students approaching research, but it will also be a helpful and ready-to-use tool to the mature researcher. After collecting some classical material about the geometry of the hyperbolic space and the Teichmüller space, the book centers on the two fundamental results: Mostow's rigidity theorem (of which a complete proof is given following Gromov and Thurston) and Margulis' lemma. These results form the basis for the study of the space of the hyperbolic manifolds in all dimensions (Chabauty and geometric topology); a unified exposition is given of Wang's theorem and the Jorgensen-Thurston theory. A large part is devoted to the three-dimensional case: a complete and elementary proof of the hyperbolic surgery theorem is given based on the possibility of representing three manifolds as glued ideal tetrahedra. The last chapter deals with some related ideas and generalizations (bounded cohomology, flat fiber bundles, amenable groups). This is the first book to collect this material together from numerous scattered sources to give a detailed presentation at a unified level accessible to novice readers |
| Beschreibung: | 1 Online-Ressource (XIV, 332p. 175 illus) |
| ISBN: | 9783642581588 9783540555346 |
| ISSN: | 0172-5939 |
| DOI: | 10.1007/978-3-642-58158-8 |
Internformat
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| 245 | 1 | 0 | |a Lectures on Hyperbolic Geometry |c by Riccardo Benedetti, Carlo Petronio |
| 264 | 1 | |a Berlin, Heidelberg |b Springer Berlin Heidelberg |c 1992 | |
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| 650 | 4 | |a Mathematics | |
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Datensatz im Suchindex
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| author | Benedetti, Riccardo |
| author_facet | Benedetti, Riccardo |
| author_role | aut |
| author_sort | Benedetti, Riccardo |
| author_variant | r b rb |
| building | Verbundindex |
| bvnumber | BV042422713 |
| classification_tum | MAT 000 |
| collection | ZDB-2-SMA ZDB-2-BAE |
| ctrlnum | (OCoLC)1184290022 (DE-599)BVBBV042422713 |
| dewey-full | 516.36 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 516 - Geometry |
| dewey-raw | 516.36 |
| dewey-search | 516.36 |
| dewey-sort | 3516.36 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-3-642-58158-8 |
| format | Electronic eBook |
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| id | DE-604.BV042422713 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:11Z |
| institution | BVB |
| isbn | 9783642581588 9783540555346 |
| issn | 0172-5939 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027858130 |
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| physical | 1 Online-Ressource (XIV, 332p. 175 illus) |
| psigel | ZDB-2-SMA ZDB-2-BAE ZDB-2-SMA_Archive |
| publishDate | 1992 |
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| publisher | Springer Berlin Heidelberg |
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| series2 | Universitext |
| spelling | Benedetti, Riccardo Verfasser aut Lectures on Hyperbolic Geometry by Riccardo Benedetti, Carlo Petronio Berlin, Heidelberg Springer Berlin Heidelberg 1992 1 Online-Ressource (XIV, 332p. 175 illus) txt rdacontent c rdamedia cr rdacarrier Universitext 0172-5939 In recent years hyperbolic geometry has been the object and the preparation for extensive study that has produced important and often amazing results and also opened up new questions. The book concerns the geometry of manifolds and in particular hyperbolic manifolds; its aim is to provide an exposition of some fundamental results, and to be as far as possible self-contained, complete, detailed and unified. Since it starts from the basics and it reaches recent developments of the theory, the book is mainly addressed to graduate-level students approaching research, but it will also be a helpful and ready-to-use tool to the mature researcher. After collecting some classical material about the geometry of the hyperbolic space and the Teichmüller space, the book centers on the two fundamental results: Mostow's rigidity theorem (of which a complete proof is given following Gromov and Thurston) and Margulis' lemma. These results form the basis for the study of the space of the hyperbolic manifolds in all dimensions (Chabauty and geometric topology); a unified exposition is given of Wang's theorem and the Jorgensen-Thurston theory. A large part is devoted to the three-dimensional case: a complete and elementary proof of the hyperbolic surgery theorem is given based on the possibility of representing three manifolds as glued ideal tetrahedra. The last chapter deals with some related ideas and generalizations (bounded cohomology, flat fiber bundles, amenable groups). This is the first book to collect this material together from numerous scattered sources to give a detailed presentation at a unified level accessible to novice readers Mathematics Global differential geometry Differential Geometry Mathematik Hyperbolische Geometrie (DE-588)4161041-6 gnd rswk-swf Hyperbolische Geometrie (DE-588)4161041-6 s 1\p DE-604 Petronio, Carlo Sonstige oth https://doi.org/10.1007/978-3-642-58158-8 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Benedetti, Riccardo Lectures on Hyperbolic Geometry Mathematics Global differential geometry Differential Geometry Mathematik Hyperbolische Geometrie (DE-588)4161041-6 gnd |
| subject_GND | (DE-588)4161041-6 |
| title | Lectures on Hyperbolic Geometry |
| title_auth | Lectures on Hyperbolic Geometry |
| title_exact_search | Lectures on Hyperbolic Geometry |
| title_full | Lectures on Hyperbolic Geometry by Riccardo Benedetti, Carlo Petronio |
| title_fullStr | Lectures on Hyperbolic Geometry by Riccardo Benedetti, Carlo Petronio |
| title_full_unstemmed | Lectures on Hyperbolic Geometry by Riccardo Benedetti, Carlo Petronio |
| title_short | Lectures on Hyperbolic Geometry |
| title_sort | lectures on hyperbolic geometry |
| topic | Mathematics Global differential geometry Differential Geometry Mathematik Hyperbolische Geometrie (DE-588)4161041-6 gnd |
| topic_facet | Mathematics Global differential geometry Differential Geometry Mathematik Hyperbolische Geometrie |
| url | https://doi.org/10.1007/978-3-642-58158-8 |
| work_keys_str_mv | AT benedettiriccardo lecturesonhyperbolicgeometry AT petroniocarlo lecturesonhyperbolicgeometry |