The Arithmetic of Hyperbolic 3-Manifolds:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
New York, NY
Springer New York
2003
|
| Schriftenreihe: | Graduate Texts in Mathematics
219 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | For the past 25 years, the Geometrization Program of Thurston has been a driving force for research in 3-manifold topology. This has inspired a surge of activity investigating hyperbolic 3-manifolds (and Kleinian groups), as these manifolds form the largest and least well-understood class of compact 3-manifolds. Familiar and new tools from diverse areas of mathematics have been utilized in these investigations, from topology, geometry, analysis, group theory, and from the point of view of this book, algebra and number theory. This book is aimed at readers already familiar with the basics of hyperbolic 3-manifolds or Kleinian groups, and it is intended to introduce them to the interesting connections with number theory and the tools that will be required to pursue them. While there are a number of texts which cover the topological, geometric and analytical aspects of hyperbolic 3-manifolds, this book is unique in that it deals exclusively with the arithmetic aspects, which are not covered in other texts. Colin Maclachlan is a Reader in the Department of Mathematical Sciences at the University of Aberdeen in Scotland where he has served since 1968. He is a former President of the Edinburgh Mathematical Society. Alan Reid is a Professor in the Department of Mathematics at The University of Texas at Austin. He is a former Royal Society University Research Fellow, Alfred P. Sloan Fellow and winner of the Sir Edmund Whittaker Prize from The Edinburgh Mathematical Society. Both authors have published extensively in the general area of discrete groups, hyperbolic manifolds and low-dimensional topology |
| Beschreibung: | 1 Online-Ressource (XIII, 467 p) |
| ISBN: | 9781475767209 9781441931221 |
| ISSN: | 0072-5285 |
| DOI: | 10.1007/978-1-4757-6720-9 |
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| 500 | |a For the past 25 years, the Geometrization Program of Thurston has been a driving force for research in 3-manifold topology. This has inspired a surge of activity investigating hyperbolic 3-manifolds (and Kleinian groups), as these manifolds form the largest and least well-understood class of compact 3-manifolds. Familiar and new tools from diverse areas of mathematics have been utilized in these investigations, from topology, geometry, analysis, group theory, and from the point of view of this book, algebra and number theory. This book is aimed at readers already familiar with the basics of hyperbolic 3-manifolds or Kleinian groups, and it is intended to introduce them to the interesting connections with number theory and the tools that will be required to pursue them. While there are a number of texts which cover the topological, geometric and analytical aspects of hyperbolic 3-manifolds, this book is unique in that it deals exclusively with the arithmetic aspects, which are not covered in other texts. Colin Maclachlan is a Reader in the Department of Mathematical Sciences at the University of Aberdeen in Scotland where he has served since 1968. He is a former President of the Edinburgh Mathematical Society. Alan Reid is a Professor in the Department of Mathematics at The University of Texas at Austin. He is a former Royal Society University Research Fellow, Alfred P. Sloan Fellow and winner of the Sir Edmund Whittaker Prize from The Edinburgh Mathematical Society. Both authors have published extensively in the general area of discrete groups, hyperbolic manifolds and low-dimensional topology | ||
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Datensatz im Suchindex
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| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 514 - Topology |
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| discipline | Mathematik |
| doi_str_mv | 10.1007/978-1-4757-6720-9 |
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| isbn | 9781475767209 9781441931221 |
| issn | 0072-5285 |
| language | English |
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| spelling | Maclachlan, Colin Verfasser aut The Arithmetic of Hyperbolic 3-Manifolds by Colin Maclachlan, Alan W. Reid New York, NY Springer New York 2003 1 Online-Ressource (XIII, 467 p) txt rdacontent c rdamedia cr rdacarrier Graduate Texts in Mathematics 219 0072-5285 For the past 25 years, the Geometrization Program of Thurston has been a driving force for research in 3-manifold topology. This has inspired a surge of activity investigating hyperbolic 3-manifolds (and Kleinian groups), as these manifolds form the largest and least well-understood class of compact 3-manifolds. Familiar and new tools from diverse areas of mathematics have been utilized in these investigations, from topology, geometry, analysis, group theory, and from the point of view of this book, algebra and number theory. This book is aimed at readers already familiar with the basics of hyperbolic 3-manifolds or Kleinian groups, and it is intended to introduce them to the interesting connections with number theory and the tools that will be required to pursue them. While there are a number of texts which cover the topological, geometric and analytical aspects of hyperbolic 3-manifolds, this book is unique in that it deals exclusively with the arithmetic aspects, which are not covered in other texts. Colin Maclachlan is a Reader in the Department of Mathematical Sciences at the University of Aberdeen in Scotland where he has served since 1968. He is a former President of the Edinburgh Mathematical Society. Alan Reid is a Professor in the Department of Mathematics at The University of Texas at Austin. He is a former Royal Society University Research Fellow, Alfred P. Sloan Fellow and winner of the Sir Edmund Whittaker Prize from The Edinburgh Mathematical Society. Both authors have published extensively in the general area of discrete groups, hyperbolic manifolds and low-dimensional topology Mathematics Geometry Number theory Cell aggregation / Mathematics Manifolds and Cell Complexes (incl. Diff.Topology) Number Theory Mathematik Kleinsche Gruppe (DE-588)4164159-0 gnd rswk-swf Hyperbolische Mannigfaltigkeit (DE-588)4161044-1 gnd rswk-swf Dimension 3 (DE-588)4321722-9 gnd rswk-swf Hyperbolische Mannigfaltigkeit (DE-588)4161044-1 s Dimension 3 (DE-588)4321722-9 s Kleinsche Gruppe (DE-588)4164159-0 s 1\p DE-604 Reid, Alan W. Sonstige oth https://doi.org/10.1007/978-1-4757-6720-9 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Maclachlan, Colin The Arithmetic of Hyperbolic 3-Manifolds Mathematics Geometry Number theory Cell aggregation / Mathematics Manifolds and Cell Complexes (incl. Diff.Topology) Number Theory Mathematik Kleinsche Gruppe (DE-588)4164159-0 gnd Hyperbolische Mannigfaltigkeit (DE-588)4161044-1 gnd Dimension 3 (DE-588)4321722-9 gnd |
| subject_GND | (DE-588)4164159-0 (DE-588)4161044-1 (DE-588)4321722-9 |
| title | The Arithmetic of Hyperbolic 3-Manifolds |
| title_auth | The Arithmetic of Hyperbolic 3-Manifolds |
| title_exact_search | The Arithmetic of Hyperbolic 3-Manifolds |
| title_full | The Arithmetic of Hyperbolic 3-Manifolds by Colin Maclachlan, Alan W. Reid |
| title_fullStr | The Arithmetic of Hyperbolic 3-Manifolds by Colin Maclachlan, Alan W. Reid |
| title_full_unstemmed | The Arithmetic of Hyperbolic 3-Manifolds by Colin Maclachlan, Alan W. Reid |
| title_short | The Arithmetic of Hyperbolic 3-Manifolds |
| title_sort | the arithmetic of hyperbolic 3 manifolds |
| topic | Mathematics Geometry Number theory Cell aggregation / Mathematics Manifolds and Cell Complexes (incl. Diff.Topology) Number Theory Mathematik Kleinsche Gruppe (DE-588)4164159-0 gnd Hyperbolische Mannigfaltigkeit (DE-588)4161044-1 gnd Dimension 3 (DE-588)4321722-9 gnd |
| topic_facet | Mathematics Geometry Number theory Cell aggregation / Mathematics Manifolds and Cell Complexes (incl. Diff.Topology) Number Theory Mathematik Kleinsche Gruppe Hyperbolische Mannigfaltigkeit Dimension 3 |
| url | https://doi.org/10.1007/978-1-4757-6720-9 |
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