The Resource Foundations of hyperbolic manifolds, John G. Ratcliffe, (electronic book)
Foundations of hyperbolic manifolds, John G. Ratcliffe, (electronic book)
Resource Information
The item Foundations of hyperbolic manifolds, John G. Ratcliffe, (electronic book) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Liverpool.This item is available to borrow from 1 library branch.
Resource Information
The item Foundations of hyperbolic manifolds, John G. Ratcliffe, (electronic book) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Liverpool.
This item is available to borrow from 1 library branch.
 Summary
 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. The book is divided into three parts. The first part is concerned with hyperbolic geometry and discrete groups. The main results are the characterization of hyperbolic reflection groups and Euclidean crystallographic groups. The second part is devoted to the theory of hyperbolic manifolds. The main results are Mostow's rigidity theorem and the determination of the global geometry of hyperbolic manifolds of finite volume. The third part integrates the first two parts in a development of the theory of hyperbolic orbifolds. The main result is Poincare<<s fundamental polyhedron theorem. The exposition if at the level of a second year graduate student with particular emphasis placed on readability and completeness of argument. After reading this book, the reader will have the necessary background to study the current research on hyperbolic manifolds. The second edition is a thorough revision of the first edition that embodies hundreds of changes, corrections, and additions, including over sixty new lemmas, theorems, and corollaries. The new main results are Schl\¬afli's differential formula and the $n$dimensional GaussBonnet theorem. John G. Ratcliffe is a Professor of Mathematics at Vanderbilt University
 Language
 eng
 Edition
 2nd ed.
 Extent
 1 online resource (xii, 779 pages)
 Contents

 Euclidean Geometry
 Spherical Geometry
 Hyperbolic Geometry
 Inversive Geometry
 Isometries of Hyperbolic Space
 Geometry of Discrete Groups
 Classical Discrete Groups
 Geometric Manifolds
 Geometric Surfaces
 Hyperbolic 3Manifolds
 Hyperbolic nManifolds
 Geometrically Finite nManifolds
 Geometric Orbifolds
 Isbn
 9780387331973
 Label
 Foundations of hyperbolic manifolds
 Title
 Foundations of hyperbolic manifolds
 Statement of responsibility
 John G. Ratcliffe
 Language
 eng
 Summary
 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. The book is divided into three parts. The first part is concerned with hyperbolic geometry and discrete groups. The main results are the characterization of hyperbolic reflection groups and Euclidean crystallographic groups. The second part is devoted to the theory of hyperbolic manifolds. The main results are Mostow's rigidity theorem and the determination of the global geometry of hyperbolic manifolds of finite volume. The third part integrates the first two parts in a development of the theory of hyperbolic orbifolds. The main result is Poincare<<s fundamental polyhedron theorem. The exposition if at the level of a second year graduate student with particular emphasis placed on readability and completeness of argument. After reading this book, the reader will have the necessary background to study the current research on hyperbolic manifolds. The second edition is a thorough revision of the first edition that embodies hundreds of changes, corrections, and additions, including over sixty new lemmas, theorems, and corollaries. The new main results are Schl\¬afli's differential formula and the $n$dimensional GaussBonnet theorem. John G. Ratcliffe is a Professor of Mathematics at Vanderbilt University
 Cataloging source
 GW5XE
 http://library.link/vocab/creatorDate
 1948
 http://library.link/vocab/creatorName
 Ratcliffe, John G.
 Dewey number
 516.9
 Illustrations
 illustrations
 Index
 index present
 LC call number
 QA685
 LC item number
 .R22 2006eb
 Literary form
 non fiction
 Nature of contents

 dictionaries
 bibliography
 Series statement
 Graduate texts in mathematics
 Series volume
 149
 http://library.link/vocab/subjectName

 Geometry, Hyperbolic
 Hyperbolic spaces
 Label
 Foundations of hyperbolic manifolds, John G. Ratcliffe, (electronic book)
 Bibliography note
 Includes bibliographical references (pages 745767) and index
 Carrier category
 online resource
 Carrier category code

 cr
 Carrier MARC source
 rdacarrier
 Color
 multicolored
 Content category
 text
 Content type code

 txt
 Content type MARC source
 rdacontent
 Contents
 Euclidean Geometry  Spherical Geometry  Hyperbolic Geometry  Inversive Geometry  Isometries of Hyperbolic Space  Geometry of Discrete Groups  Classical Discrete Groups  Geometric Manifolds  Geometric Surfaces  Hyperbolic 3Manifolds  Hyperbolic nManifolds  Geometrically Finite nManifolds  Geometric Orbifolds
 Control code
 SPR184923688
 Dimensions
 unknown
 Edition
 2nd ed.
 Extent
 1 online resource (xii, 779 pages)
 Form of item
 online
 Isbn
 9780387331973
 Media category
 computer
 Media MARC source
 rdamedia
 Media type code

 c
 Other control number
 10.1007/9780387473222
 Other physical details
 illustrations.
 Specific material designation
 remote
 Label
 Foundations of hyperbolic manifolds, John G. Ratcliffe, (electronic book)
 Bibliography note
 Includes bibliographical references (pages 745767) and index
 Carrier category
 online resource
 Carrier category code

 cr
 Carrier MARC source
 rdacarrier
 Color
 multicolored
 Content category
 text
 Content type code

 txt
 Content type MARC source
 rdacontent
 Contents
 Euclidean Geometry  Spherical Geometry  Hyperbolic Geometry  Inversive Geometry  Isometries of Hyperbolic Space  Geometry of Discrete Groups  Classical Discrete Groups  Geometric Manifolds  Geometric Surfaces  Hyperbolic 3Manifolds  Hyperbolic nManifolds  Geometrically Finite nManifolds  Geometric Orbifolds
 Control code
 SPR184923688
 Dimensions
 unknown
 Edition
 2nd ed.
 Extent
 1 online resource (xii, 779 pages)
 Form of item
 online
 Isbn
 9780387331973
 Media category
 computer
 Media MARC source
 rdamedia
 Media type code

 c
 Other control number
 10.1007/9780387473222
 Other physical details
 illustrations.
 Specific material designation
 remote
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<div class="citation" vocab="http://schema.org/"><i class="fa faexternallinksquare fafw"></i> Data from <span resource="http://link.liverpool.ac.uk/portal/FoundationsofhyperbolicmanifoldsJohnG./KDoQJAqBj7Y/" typeof="Book http://bibfra.me/vocab/lite/Item"><span property="name http://bibfra.me/vocab/lite/label"><a href="http://link.liverpool.ac.uk/portal/FoundationsofhyperbolicmanifoldsJohnG./KDoQJAqBj7Y/">Foundations of hyperbolic manifolds, John G. Ratcliffe, (electronic book)</a></span>  <span property="potentialAction" typeOf="OrganizeAction"><span property="agent" typeof="LibrarySystem http://library.link/vocab/LibrarySystem" resource="http://link.liverpool.ac.uk/"><span property="name http://bibfra.me/vocab/lite/label"><a property="url" href="http://link.liverpool.ac.uk/">University of Liverpool</a></span></span></span></span></div>