The arithmetic of hyperbolic three-manifolds

✍ Scribed by Colin Maclachlan, Alan W. Reid

• Publisher: Springer
• Year: 2003
• Tongue: English
• Leaves: 467
• Series: Graduate texts in mathematics 219
• Edition: 2003
• Category: Library

✦ Synopsis

Recently there has been considerable interest in developing techniques based on number theory to attack problems of 3-manifolds; Contains many examples and lots of problems; Brings together much of the existing literature of Kleinian groups in a clear and concise way; At present no such text exists

✦ Table of Contents

Content: Number Theoretic Menagerie.- Kleinian Groups and Hyperbolic Manifolds.- Quaternion Algebras I.- Invariant Trace Fields.- Examples.- Applications.- Orders in Quaternion Algebras.- Quaternion Algebras II.- Arithmetic Kleinian Groups.- Arithmetic Hyperbolic 3-Manifolds and Orbifolds.- Discrete Arithmetic Groups.- Commensurate Arithmetic Groups and Volumes.- Length and Torsion in Arithmetic Hyperbolic Orbifolds.- Appendices.- References.- Index.

✦ Subjects

Three-manifolds (Topology) Variétés topologiques à 3 dimensions. Grupos hiperbolicos. Geometria diferencial.