Kleinian Groups which Are Limits of Geometrically Finite Groups PDF Download

Author: Ken'ichi Ōshika
Publisher: American Mathematical Soc.
ISBN: 0821837729
Category : Mathematics
Languages : en
Pages : 136

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Book Description
Ahlfors conjectured in 1964 that the limit set of every finitely generated Kleinian group either has Lebesgue measure $0$ or is the entire $S^2$. This title intends to prove that this conjecture is true for purely loxodromic Kleinian groups which are algebraic limits of geometrically finite groups.

Author: William P. Thurston
Publisher: American Mathematical Society
ISBN: 1470474743
Category : Mathematics
Languages : en
Pages : 337

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Book Description
William Thurston's work has had a profound influence on mathematics. He connected whole mathematical subjects in entirely new ways and changed the way mathematicians think about geometry, topology, foliations, group theory, dynamical systems, and the way these areas interact. His emphasis on understanding and imagination in mathematical learning and thinking are integral elements of his distinctive legacy. This four-part collection brings together in one place Thurston's major writings, many of which are appearing in publication for the first time. Volumes I–III contain commentaries by the Editors. Volume IV includes a preface by Steven P. Kerckhoff. Volume IV contains Thurston's highly influential, though previously unpublished, 1977–78 Princeton Course Notes on the Geometry and Topology of 3-manifolds. It is an indispensable part of the Thurston collection but can also be used on its own as a textbook or for self-study.

Author: William H. Jaco
Publisher: American Mathematical Soc.
ISBN: 0821822209
Category : Fiber spaces
Languages : en
Pages : 204

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Book Description
The main theorem of this monograph, or rather the "absolute" case of the main theorem, provides what is essentially a homotopy-classification of suitably "nondegenerate" maps of Seifert-fibered 3-manifolds into a sufficiently-large, compact, irreducible, orientable 3-manifold M.

Author: Bernard Maskit
Publisher: Springer Science & Business Media
ISBN: 3642615902
Category : Mathematics
Languages : en
Pages : 339

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Book Description
The modern theory of Kleinian groups starts with the work of Lars Ahlfors and Lipman Bers; specifically with Ahlfors' finiteness theorem, and Bers' observation that their joint work on the Beltrami equation has deep implications for the theory of Kleinian groups and their deformations. From the point of view of uniformizations of Riemann surfaces, Bers' observation has the consequence that the question of understanding the different uniformizations of a finite Riemann surface poses a purely topological problem; it is independent of the conformal structure on the surface. The last two chapters here give a topological description of the set of all (geometrically finite) uniformizations of finite Riemann surfaces. We carefully skirt Ahlfors' finiteness theorem. For groups which uniformize a finite Riemann surface; that is, groups with an invariant component, one can either start with the assumption that the group is finitely generated, and then use the finiteness theorem to conclude that the group represents only finitely many finite Riemann surfaces, or, as we do here, one can start with the assumption that, in the invariant component, the group represents a finite Riemann surface, and then, using essentially topological techniques, reach the same conclusion. More recently, Bill Thurston wrought a revolution in the field by showing that one could analyze Kleinian groups using 3-dimensional hyperbolic geome try, and there is now an active school of research using these methods.

Author: Yair N. Minsky
Publisher: Cambridge University Press
ISBN: 1139447211
Category : Mathematics
Languages : en
Pages : 399

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Book Description
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.

Author: 野水克己
Publisher: American Mathematical Soc.
ISBN: 9780821827802
Category : Mathematical analysis
Languages : en
Pages : 148

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Book Description
This volume contains papers that originally appeared in Japanese in the journal Sugaku. Ordinarily the papers would appear in the AMS translation of that journal, but to expedite publication, the Society has chosen to publish them as a volume of selected papers. The papers here are in the general area of mathematical analysis as it pertains to free probability theory.

Author: A. Marden
Publisher: Cambridge University Press
ISBN: 1139463764
Category : Mathematics
Languages : en
Pages : 393

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Book Description
We live in a three-dimensional space; what sort of space is it? Can we build it from simple geometric objects? The answers to such questions have been found in the last 30 years, and Outer Circles describes the basic mathematics needed for those answers as well as making clear the grand design of the subject of hyperbolic manifolds as a whole. The purpose of Outer Circles is to provide an account of the contemporary theory, accessible to those with minimal formal background in topology, hyperbolic geometry, and complex analysis. The text explains what is needed, and provides the expertise to use the primary tools to arrive at a thorough understanding of the big picture. This picture is further filled out by numerous exercises and expositions at the ends of the chapters and is complemented by a profusion of high quality illustrations. There is an extensive bibliography for further study.

Author: V. I. Bernik
Publisher: Cambridge University Press
ISBN: 9780521432757
Category : Mathematics
Languages : en
Pages : 198

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Book Description
This book is concerned with Diophantine approximation on smooth manifolds embedded in Euclidean space, and its aim is to develop a coherent body of theory comparable with that which already exists for classical Diophantine approximation. In particular, this book deals with Khintchine-type theorems and with the Hausdorff dimension of the associated null sets. All researchers with an interest in Diophantine approximation will welcome this book.

Author: William Mark Goldman
Publisher: American Mathematical Soc.
ISBN: 0821850822
Category : Mathematics
Languages : en
Pages : 330

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Book Description
Contains papers based on talks delivered at the AMS-IMS-SIAM Summer Research Conference on the Geometry of Group Representations, held at the University of Colorado in Boulder in July 1987. This work offers an understanding of the state of research in the geometry of group representations and their applications.

Author: R. D. Canary
Publisher: Cambridge University Press
ISBN: 9781139447195
Category : Mathematics
Languages : en
Pages : 356

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Book Description
Presents reissued articles from two classic sources on hyperbolic manifolds. Part I is an exposition of Chapters 8 and 9 of Thurston's pioneering Princeton Notes; there is a new introduction describing recent advances, with an up-to-date bibliography, giving a contemporary context in which the work can be set. Part II expounds the theory of convex hull boundaries and their bending laminations. A new appendix describes recent work. Part III is Thurston's famous paper that presents the notion of earthquakes in hyperbolic geometry and proves the earthquake theorem. The final part introduces the theory of measures on the limit set, drawing attention to related ergodic theory and the exponent of convergence. The book will be welcomed by graduate students and professional mathematicians who want a rigorous introduction to some basic tools essential for the modern theory of hyperbolic manifolds.