The Geometry of Discrete Groups (Graduate Texts in Mathematics): 91 - Softcover
Zu dieser ISBN ist aktuell kein Angebot verfügbar.
Alle Exemplare der Ausgabe mit dieser ISBN anzeigen:
Book by Beardon Alan F
Die Inhaltsangabe kann sich auf eine andere Ausgabe dieses Titels beziehen.
Reseña del editor:
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 geo metrical ideas to be found in that manuscript, as well as some more recent material. The text has been written with the conviction that geometrical explana tions 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.
Reseña del editor:
This text is about the geometric theory of discrete groups and the associated tesselations of the underlying space. The theory of Möbius transformations in n-dimensional Euclidean space is developed. These transformations are discussed as isometries of hyperbolic space and are then identified with the elementary transformations of complex analysis. A detailed account of analytic hyperbolic trigonometry is given, and this forms the basis of the subsequent analysis of tesselations of the hyperbolic plane. Emphasis is placed on the geometrical aspects of the subject and on the universal constraints which must be satisfied by all tesselations.
„Über diesen Titel“ kann sich auf eine andere Ausgabe dieses Titels beziehen.
- VerlagSpringer
- Erscheinungsdatum2012
- ISBN 10 1461270227
- ISBN 13 9781461270225
- EinbandTapa blanda
- Anzahl der Seiten356
Neu kaufen
Mehr zu diesem Angebot erfahren
EUR 74,00
Versand:
EUR 32,99
Von Deutschland nach USA
Beste Suchergebnisse beim ZVAB
Foto des Verkäufers
The Geometry of Discrete Groups
Verlag:
Springer New York
(2012)
ISBN 10: 1461270227
ISBN 13: 9781461270225
Neu
Taschenbuch
Anzahl: 1
Anbieter:
Bewertung
Buchbeschreibung Taschenbuch. Zustand: Neu. Druck auf Anfrage Neuware - Printed after ordering - 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 geo metrical ideas to be found in that manuscript, as well as some more recent material. The text has been written with the conviction that geometrical explana tions 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. Artikel-Nr. 9781461270225
Weitere Informationen zu diesem Verkäufer | Verkäufer kontaktieren
Neu kaufen
EUR 74,00
Währung umrechnen