Foundations of Hyperbolic Manifolds:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
New York, NY
Springer New York
1994
|
| Schriftenreihe: | Graduate Texts in Mathematics
149 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | This book is an exposition of the theoretical foundations of hyperbolic manifolds. It is intended to be used both as a textbook and as a reference. Particular emphasis has been placed on readability and completeness of ar gument. The treatment of the material is for the most part elementary and self-contained. The reader is assumed to have a basic knowledge of algebra and topology at the first-year graduate level of an American university. The book is divided into three parts. The first part, consisting of Chap ters 1-7, is concerned with hyperbolic geometry and basic properties of discrete groups of isometries of hyperbolic space. The main results are the existence theorem for discrete reflection groups, the Bieberbach theorems, and Selberg's lemma. The second part, consisting of Chapters 8-12, is de voted to the theory of hyperbolic manifolds. The main results are Mostow's rigidity theorem and the determination of the structure of geometrically finite hyperbolic manifolds. The third part, consisting of Chapter 13, in tegrates the first two parts in a development of the theory of hyperbolic orbifolds. The main results are the construction of the universal orbifold covering space and Poincare's fundamental polyhedron theorem |
| Beschreibung: | 1 Online-Ressource (XI, 750 p) |
| ISBN: | 9781475740134 9780387943480 |
| ISSN: | 0072-5285 |
| DOI: | 10.1007/978-1-4757-4013-4 |
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Datensatz im Suchindex
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| discipline | Mathematik |
| doi_str_mv | 10.1007/978-1-4757-4013-4 |
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| isbn | 9781475740134 9780387943480 |
| issn | 0072-5285 |
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| spelling | Ratcliffe, John G. Verfasser aut Foundations of Hyperbolic Manifolds by John G. Ratcliffe New York, NY Springer New York 1994 1 Online-Ressource (XI, 750 p) txt rdacontent c rdamedia cr rdacarrier Graduate Texts in Mathematics 149 0072-5285 This book is an exposition of the theoretical foundations of hyperbolic manifolds. It is intended to be used both as a textbook and as a reference. Particular emphasis has been placed on readability and completeness of ar gument. The treatment of the material is for the most part elementary and self-contained. The reader is assumed to have a basic knowledge of algebra and topology at the first-year graduate level of an American university. The book is divided into three parts. The first part, consisting of Chap ters 1-7, is concerned with hyperbolic geometry and basic properties of discrete groups of isometries of hyperbolic space. The main results are the existence theorem for discrete reflection groups, the Bieberbach theorems, and Selberg's lemma. The second part, consisting of Chapters 8-12, is de voted to the theory of hyperbolic manifolds. The main results are Mostow's rigidity theorem and the determination of the structure of geometrically finite hyperbolic manifolds. The third part, consisting of Chapter 13, in tegrates the first two parts in a development of the theory of hyperbolic orbifolds. The main results are the construction of the universal orbifold covering space and Poincare's fundamental polyhedron theorem Mathematics Geometry, algebraic Geometry Topology Algebraic Geometry Mathematik Hyperbolische Mannigfaltigkeit (DE-588)4161044-1 gnd rswk-swf Mannigfaltigkeit (DE-588)4037379-4 gnd rswk-swf Hyperbolische Geometrie (DE-588)4161041-6 gnd rswk-swf Hyperbolische Geometrie (DE-588)4161041-6 s 1\p DE-604 Hyperbolische Mannigfaltigkeit (DE-588)4161044-1 s 2\p DE-604 Mannigfaltigkeit (DE-588)4037379-4 s 3\p DE-604 https://doi.org/10.1007/978-1-4757-4013-4 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 | Ratcliffe, John G. Foundations of Hyperbolic Manifolds Mathematics Geometry, algebraic Geometry Topology Algebraic Geometry Mathematik Hyperbolische Mannigfaltigkeit (DE-588)4161044-1 gnd Mannigfaltigkeit (DE-588)4037379-4 gnd Hyperbolische Geometrie (DE-588)4161041-6 gnd |
| subject_GND | (DE-588)4161044-1 (DE-588)4037379-4 (DE-588)4161041-6 |
| title | Foundations of Hyperbolic Manifolds |
| title_auth | Foundations of Hyperbolic Manifolds |
| title_exact_search | Foundations of Hyperbolic Manifolds |
| title_full | Foundations of Hyperbolic Manifolds by John G. Ratcliffe |
| title_fullStr | Foundations of Hyperbolic Manifolds by John G. Ratcliffe |
| title_full_unstemmed | Foundations of Hyperbolic Manifolds by John G. Ratcliffe |
| title_short | Foundations of Hyperbolic Manifolds |
| title_sort | foundations of hyperbolic manifolds |
| topic | Mathematics Geometry, algebraic Geometry Topology Algebraic Geometry Mathematik Hyperbolische Mannigfaltigkeit (DE-588)4161044-1 gnd Mannigfaltigkeit (DE-588)4037379-4 gnd Hyperbolische Geometrie (DE-588)4161041-6 gnd |
| topic_facet | Mathematics Geometry, algebraic Geometry Topology Algebraic Geometry Mathematik Hyperbolische Mannigfaltigkeit Mannigfaltigkeit Hyperbolische Geometrie |
| url | https://doi.org/10.1007/978-1-4757-4013-4 |
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