The Global Topology Of Deformation Spaces Of Kleinian Groups
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Spaces of Kleinian Groups
| Author | : Yair N. Minsky |
| Publisher | : Cambridge University Press |
| Total Pages | : 399 |
| Release | : 2006-06-19 |
| Genre | : Mathematics |
| ISBN | : 1139447211 |
The subject of Kleinian groups and hyperbolic 3-manifolds is currently undergoing explosively fast development. This volume contains important expositions on topics such as topology and geometry of 3-manifolds, curve complexes, classical Ahlfors-Bers theory and computer explorations. Researchers in these and related areas will find much of interest here.
Topology '90
| Author | : Boris N. Apanasov |
| Publisher | : Walter de Gruyter |
| Total Pages | : 473 |
| Release | : 2011-10-13 |
| Genre | : Mathematics |
| ISBN | : 3110857723 |
This series is devoted to the publication of monographs, lecture resp. seminar notes, and other materials arising from programs of the OSU Mathemaical Research Institute. This includes proceedings of conferences or workshops held at the Institute, and other mathematical writings.
Hyperbolic Manifolds and Kleinian Groups
| Author | : Katsuhiko Matsuzaki |
| Publisher | : Clarendon Press |
| Total Pages | : 265 |
| Release | : 1998-04-30 |
| Genre | : Mathematics |
| ISBN | : 0191591203 |
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.
Topology And Teichmuller Spaces - Proceedings Of The 37th Taniguchi Symposium
| Author | : Sadayoshi Kojima |
| Publisher | : World Scientific |
| Total Pages | : 305 |
| Release | : 1996-11-09 |
| Genre | : |
| ISBN | : 981460254X |
This proceedings is a collection of articles on Topology and Teichmüller Spaces. Special emphasis is being put on the universal Teichmüller space, the topology of moduli of algebraic curves, the space of representations of discrete groups, Kleinian groups and Dehn filling deformations, the geometry of Riemann surfaces, and some related topics.
Conformal Geometry of Discrete Groups and Manifolds
| Author | : Boris N. Apanasov |
| Publisher | : Walter de Gruyter |
| Total Pages | : 541 |
| Release | : 2011-06-24 |
| Genre | : Mathematics |
| ISBN | : 3110808056 |
The aim of the Expositions is to present new and important developments in pure and applied mathematics. Well established in the community over more than two decades, the series offers a large library of mathematical works, including several important classics. The volumes supply thorough and detailed expositions of the methods and ideas essential to the topics in question. In addition, they convey their relationships to other parts of mathematics. The series is addressed to advanced readers interested in a thorough study of the subject. Editorial Board Lev Birbrair, Universidade Federal do Ceará, Fortaleza, Brasil Walter D. Neumann, Columbia University, New York, USA Markus J. Pflaum, University of Colorado, Boulder, USA Dierk Schleicher, Jacobs University, Bremen, Germany Katrin Wendland, University of Freiburg, Germany Honorary Editor Victor P. Maslov, Russian Academy of Sciences, Moscow, Russia Titles in planning include Yuri A. Bahturin, Identical Relations in Lie Algebras (2019) Yakov G. Berkovich, Lev G. Kazarin, and Emmanuel M. Zhmud', Characters of Finite Groups, Volume 2 (2019) Jorge Herbert Soares de Lira, Variational Problems for Hypersurfaces in Riemannian Manifolds (2019) Volker Mayer, Mariusz Urbański, and Anna Zdunik, Random and Conformal Dynamical Systems (2021) Ioannis Diamantis, Boštjan Gabrovšek, Sofia Lambropoulou, and Maciej Mroczkowski, Knot Theory of Lens Spaces (2021)
Homotopy Equivalences of 3-Manifolds and Deformation Theory of Kleinian Groups
| Author | : Richard Douglas Canary |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 238 |
| Release | : 2004 |
| Genre | : Mathematics |
| ISBN | : 0821835491 |
Three volume narrative history of 20th century.
Complex Kleinian Groups
| Author | : Angel Cano |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 288 |
| Release | : 2012-11-05 |
| Genre | : Mathematics |
| ISBN | : 3034804814 |
This monograph lays down the foundations of the theory of complex Kleinian groups, a newly born area of mathematics whose origin traces back to the work of Riemann, Poincaré, Picard and many others. Kleinian groups are, classically, discrete groups of conformal automorphisms of the Riemann sphere, and these can be regarded too as being groups of holomorphic automorphisms of the complex projective line CP1. When going into higher dimensions, there is a dichotomy: Should we look at conformal automorphisms of the n-sphere?, or should we look at holomorphic automorphisms of higher dimensional complex projective spaces? These two theories are different in higher dimensions. In the first case we are talking about groups of isometries of real hyperbolic spaces, an area of mathematics with a long-standing tradition. In the second case we are talking about an area of mathematics that still is in its childhood, and this is the focus of study in this monograph. This brings together several important areas of mathematics, as for instance classical Kleinian group actions, complex hyperbolic geometry, chrystallographic groups and the uniformization problem for complex manifolds.
