Hyperbolic Manifolds and Kleinian Groups - Rilegato

Matsuzaki, Katsuhiko; Taniguchi, Masahiko

Rilegato

ISBN 10: 0198500629 ISBN 13: 9780198500629

Casa editrice: Clarendon Press, 1998

Riassunto

A Kleinian group is a discrete subgroup of the isometry group of hyperbolic 3-space, which is also regarded as a subgroup of Möbius transformations in the complex plane. The present book is a comprehensive guide to theories of Kleinian groups from the viewpoints of hyperbolic geometry and complex analysis. After 1960, Ahlfors and Bers were the leading researchers of Kleinian groups and helped it to become an active area of complex analysis as a branch of Teichmüller theory. Later, Thurston brought a revolution to this area with his profound investigation of hyperbolic manifolds, and at the same time complex dynamical approach was strongly developed by Sullivan. This book provides fundamental results and important theorems which are needed for access to the frontiers of the theory from a modern viewpoint.

Su questo libro

Recensione:

'The presentation of the whole theory is very nice...the book reads well, and will be interesting and accessible for mathematicians from several branches of mathematics' EMS

Contenuti:

• 0: Hyperbolic surfaces and Fuchsian groups: summary
• 1: Hyperbolic 3-manifolds
• 2: The basis of Kleinian group theory
• 3: Geometrically finite Kleinian groups
• 4: Finitely generated Kleinian groups
• 5: The sphere at infinity
• 6: Infinite ends of hyperbolic manifolds
• 7: Algebraic and geometric convergences
• Appendix
• References

Su questa edizione

• Editore: Clarendon Press
• Data di pubblicazione: 1998
• ISBN 10: 0198500629
• ISBN 13: 9780198500629
• Rilegatura: Copertina rigida
• Numero di pagine: 264