Foundations of Hyperbolic Manifolds


Author: John Ratcliffe
Publisher: Springer Science & Business Media
ISBN: 1475740131
Category: Mathematics
Page: 750
View: 7858
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This book is an exposition of the theoretical foundations of hyperbolic manifolds. It is intended to be used both as a textbook and as a reference. Particular emphasis has been placed on readability and completeness of ar gument. The treatment of the material is for the most part elementary and self-contained. The reader is assumed to have a basic knowledge of algebra and topology at the first-year graduate level of an American university. The book is divided into three parts. The first part, consisting of Chap ters 1-7, is concerned with hyperbolic geometry and basic properties of discrete groups of isometries of hyperbolic space. The main results are the existence theorem for discrete reflection groups, the Bieberbach theorems, and Selberg's lemma. The second part, consisting of Chapters 8-12, is de voted to the theory of hyperbolic manifolds. The main results are Mostow's rigidity theorem and the determination of the structure of geometrically finite hyperbolic manifolds. The third part, consisting of Chapter 13, in tegrates the first two parts in a development of the theory of hyperbolic orbifolds. The main results are the construction of the universal orbifold covering space and Poincare's fundamental polyhedron theorem.

Fundamentals of Hyperbolic Manifolds

Selected Expositions
Author: R. D. Canary,A. Marden,D. B. A. Epstein
Publisher: Cambridge University Press
ISBN: 0521615585
Category: Mathematics
Page: 335
View: 3036
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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.

Hyperbolic Manifolds


Author: Albert Marden
Publisher: Cambridge University Press
ISBN: 1107116740
Category: Mathematics
Page: 550
View: 4805
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Second edition of Outer circles, which has changed title to: Hyperbolic manifolds.

The Arithmetic of Hyperbolic 3-Manifolds


Author: Colin Maclachlan,Alan W. Reid
Publisher: Springer Science & Business Media
ISBN: 147576720X
Category: Mathematics
Page: 467
View: 8527
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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

Foundations of Differentiable Manifolds and Lie Groups


Author: Frank W. Warner
Publisher: Springer Science & Business Media
ISBN: 9780387908946
Category: Mathematics
Page: 272
View: 9025
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Foundations of Differentiable Manifolds and Lie Groups gives a clear, detailed, and careful development of the basic facts on manifold theory and Lie Groups. It includes differentiable manifolds, tensors and differentiable forms. Lie groups and homogenous spaces, integration on manifolds, and in addition provides a proof of the de Rham theorem via sheaf cohomology theory, and develops the local theory of elliptic operators culminating in a proof of the Hodge theorem. Those interested in any of the diverse areas of mathematics requiring the notion of a differentiable manifold will find this beginning graduate-level text extremely useful.

Pacific Journal of Mathematics


Author: N.A
Publisher: N.A
ISBN: N.A
Category: Mathematics
Page: N.A
View: 2998
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Choice

Publication of the Association of College and Research Libraries, a Division of the American Library Association
Author: N.A
Publisher: N.A
ISBN: N.A
Category: Academic libraries
Page: N.A
View: 8772
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On volumes of some hyperbolic 3-manifolds


Author: Andrei Vesnin
Publisher: N.A
ISBN: N.A
Category: Three-manifolds (Topology)
Page: 132
View: 952
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Journal of the Korean Mathematical Society


Author: N.A
Publisher: N.A
ISBN: N.A
Category: Mathematics
Page: N.A
View: 3568
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Indiana University Mathematics Journal


Author: N.A
Publisher: N.A
ISBN: N.A
Category: Mathematics
Page: N.A
View: 785
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Four-manifolds, geometries and knots


Author: Jonathan Arthur Hillman,University of Warwick. Mathematics Institute
Publisher: N.A
ISBN: N.A
Category: Four-manifolds (Topology)
Page: 379
View: 2030
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SIAM Journal on Control and Optimization


Author: N.A
Publisher: N.A
ISBN: N.A
Category: Control theory
Page: N.A
View: 2556
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Spherical CR geometry and Dehn surgery


Author: Richard Evan Schwartz
Publisher: Princeton Univ Pr
ISBN: 9780691128092
Category: Mathematics
Page: 186
View: 6084
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This book proves an analogue of William Thurston's celebrated hyperbolic Dehn surgery theorem in the context of complex hyperbolic discrete groups, and then derives two main geometric consequences from it. The first is the construction of large numbers of closed real hyperbolic 3-manifolds which bound complex hyperbolic orbifolds--the only known examples of closed manifolds that simultaneously have these two kinds of geometric structures. The second is a complete understanding of the structure of complex hyperbolic reflection triangle groups in cases where the angle is small. In an accessible and straightforward manner, Richard Evan Schwartz also presents a large amount of useful information on complex hyperbolic geometry and discrete groups.Schwartz relies on elementary proofs and avoids quotations of preexisting technical material as much as possible. For this reason, this book will benefit graduate students seeking entry into this emerging area of research, as well as researchers in allied fields such as Kleinian groups and CR geometry.

Revista Matemática Iberoamericana


Author: N.A
Publisher: N.A
ISBN: N.A
Category: Mathematics
Page: N.A
View: 2015
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Geometry & Topology


Author: N.A
Publisher: N.A
ISBN: N.A
Category: Geometry
Page: N.A
View: 6964
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Fully refereed international journal dealing with all aspects of geometry and topology and their applications.

Annales Scientifiques de L'École Normale Supérieure


Author: Ecole normale supérieure (France)
Publisher: N.A
ISBN: N.A
Category: Mathematics
Page: N.A
View: 1472
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Foundations of Differential Geometry


Author: Shoshichi Kobayashi,Katsumi Nomizu
Publisher: University of Texas Press
ISBN: 9780471157335
Category: Mathematics
Page: 344
View: 1796
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One of two volumes which lay the foundations for understanding differential geometry. This work familiarizes readers with various techniques of computation.

The Asian Journal of Mathematics

AJM.
Author: N.A
Publisher: N.A
ISBN: N.A
Category: Mathematics
Page: N.A
View: 3577
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