Coverart for item
The Resource Foundations of Hyperbolic Manifolds, by John G. Ratcliffe, (electronic resource)

Foundations of Hyperbolic Manifolds, by John G. Ratcliffe, (electronic resource)

Label
Foundations of Hyperbolic Manifolds
Title
Foundations of Hyperbolic Manifolds
Statement of responsibility
by 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. This third edition greatly expands upon the second with an abundance of additional content, including a section dedicated to arithmetic hyperbolic groups. Over 40 new lemmas, theorems, and corollaries feature, along with more than 70 additional exercises. Color adds a new dimension to figures throughout. 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 Poincaré’s fundamental polyhedron theorem. The exposition is 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. From reviews of the second edition: Designed to be useful as both textbook and a reference, this book renders a real service to the mathematical community by putting together the tools and prerequisites needed to enter the territory of Thurston’s formidable theory of hyperbolic 3-manifolds [...] Every chapter is followed by historical notes, with attributions to the relevant literature, both of the originators of the idea present in the chapter and of modern presentation thereof. Victor V. Pambuccian, Zentralblatt MATH, Vol. 1106 (8), 2007.--
Member of
Assigning source
Provided by publisher
http://library.link/vocab/creatorName
Ratcliffe, John G
Image bit depth
0
Literary form
non fiction
Nature of contents
dictionaries
Series statement
  • Graduate Texts in Mathematics,
  • Springer eBooks.
Series volume
149
http://library.link/vocab/subjectName
  • Geometry
  • Topology
  • Topological groups
  • Lie groups
Label
Foundations of Hyperbolic Manifolds, by John G. Ratcliffe, (electronic resource)
Link
https://eui.idm.oclc.org/login?url=https://doi.org/10.1007/978-3-030-31597-9
Instantiates
Publication
Antecedent source
mixed
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Color
not applicable
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
978-3-030-31597-9
Dimensions
unknown
Edition
3rd ed. 2019.
Extent
1 online resource (XII, 800 pages)
File format
multiple file formats
Form of item
  • online
  • electronic
Governing access note
Use of this electronic resource may be governed by a license agreement which restricts use to the European University Institute community. Each user is responsible for limiting use to individual, non-commercial purposes, without systematically downloading, distributing, or retaining substantial portions of information, provided that all copyright and other proprietary notices contained on the materials are retained. The use of software, including scripts, agents, or robots, is generally prohibited and may result in the loss of access to these resources for the entire European University Institute community
Isbn
9783030315979
Level of compression
uncompressed
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Other physical details
160 illustrations, 152 illustrations in color.
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
(OCoLC)1125947795
Label
Foundations of Hyperbolic Manifolds, by John G. Ratcliffe, (electronic resource)
Link
https://eui.idm.oclc.org/login?url=https://doi.org/10.1007/978-3-030-31597-9
Publication
Antecedent source
mixed
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Color
not applicable
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
978-3-030-31597-9
Dimensions
unknown
Edition
3rd ed. 2019.
Extent
1 online resource (XII, 800 pages)
File format
multiple file formats
Form of item
  • online
  • electronic
Governing access note
Use of this electronic resource may be governed by a license agreement which restricts use to the European University Institute community. Each user is responsible for limiting use to individual, non-commercial purposes, without systematically downloading, distributing, or retaining substantial portions of information, provided that all copyright and other proprietary notices contained on the materials are retained. The use of software, including scripts, agents, or robots, is generally prohibited and may result in the loss of access to these resources for the entire European University Institute community
Isbn
9783030315979
Level of compression
uncompressed
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Other physical details
160 illustrations, 152 illustrations in color.
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
(OCoLC)1125947795

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