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The Resource Foundations of hyperbolic manifolds, John G. Ratcliffe, (electronic book)

Foundations of hyperbolic manifolds, John G. Ratcliffe, (electronic book)

Label
Foundations of hyperbolic manifolds
Title
Foundations of hyperbolic manifolds
Statement of responsibility
John G. Ratcliffe
Creator
Subject
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\&#x00AC;afli's differential formula and the $n$-dimensional Gauss-Bonnet theorem. John G. Ratcliffe is a Professor of Mathematics at Vanderbilt University
Member of
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)
Instantiates
Publication
Bibliography note
Includes bibliographical references (pages 745-767) 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 3-Manifolds -- Hyperbolic n-Manifolds -- Geometrically Finite n-Manifolds -- 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
10.1007/978-0-387-47322-2
Other physical details
illustrations.
Specific material designation
remote
Label
Foundations of hyperbolic manifolds, John G. Ratcliffe, (electronic book)
Publication
Bibliography note
Includes bibliographical references (pages 745-767) 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 3-Manifolds -- Hyperbolic n-Manifolds -- Geometrically Finite n-Manifolds -- 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
10.1007/978-0-387-47322-2
Other physical details
illustrations.
Specific material designation
remote

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