The Resource Hyperbolic Manifolds and Discrete Groups, by Michael Kapovich, (electronic resource)

Hyperbolic Manifolds and Discrete Groups, by Michael Kapovich, (electronic resource)

Label
Hyperbolic Manifolds and Discrete Groups
Title
Hyperbolic Manifolds and Discrete Groups
Statement of responsibility
by Michael Kapovich
Creator
Author
Author
Subject
Language
  • eng
  • eng
Summary
This classic book is at the crossroads of several branches of mathematics: hyperbolic geometry, discrete groups, 3-dimensional topology, geometric group theory, and complex analysis. The main focus throughout the text is on Thurston’s hyperbolization theorem, one of the central results of 3-dimensional topology that has completely changed the landscape of the field. The book contains a number of open problems and conjectures related to the hyperbolization theorem as well as rich discussions on related topics including geometric structures on 3-manifolds, higher dimensional negatively curved manifolds, and hyperbolic groups. Featuring beautiful illustrations, a rich set of examples, numerous exercises, and an extensive bibliography and index, Hyperbolic Manifolds and Discrete Groups continues to serve as an ideal graduate text and comprehensive reference. The book is very clearly written and fairly self-contained. It will be useful to researchers and advanced graduate students in the field and can serve as an ideal guide to Thurston's work and its recent developments. ---Mathematical Reviews Beyond the hyperbolization theorem, this is an important book which had to be written; some parts are still technical and will certainly be streamlined and shortened in the next years, but together with Otal's work a complete published proof of the hyperbolization theorem is finally available. Apart from the proof itself, the book contains a lot of material which will be useful for various other directions of research. ---Zentralbatt MATH This book can act as source material for a postgraduate course and as a reference text on the topic as the references are full and extensive. ... The text is self-contained and very well illustrated. ---ASLIB Book Guide
Member of
http://library.link/vocab/creatorName
Kapovich, Michael
Dewey number
516.9
http://bibfra.me/vocab/relation/httpidlocgovvocabularyrelatorsaut
lHGXgKpykQQ
Language note
English
LC call number
QA611-614.97
Literary form
non fiction
Nature of contents
dictionaries
Series statement
Modern Birkhäuser Classics,
http://library.link/vocab/subjectName
  • Topology
  • Group theory
  • Geometry
  • Cell aggregation
  • Topology
  • Group Theory and Generalizations
  • Geometry
  • Manifolds and Cell Complexes (incl. Diff.Topology)
Label
Hyperbolic Manifolds and Discrete Groups, by Michael Kapovich, (electronic resource)
Instantiates
Publication
Note
Description based upon print version of record
Bibliography note
Includes bibliographical references and index
Carrier category
online resource
Carrier category code
cr
Content category
text
Content type code
txt
Contents
Three-Dimensional Topology -- Thurston Norm -- Geometry of Hyperbolic Space -- Kleinian Groups -- Teichmüller Theory of Riemann Surfaces -- to Orbifold Theory -- Complex Projective Structures -- Sociology of Kleinian Groups -- Ultralimits of Metric Spaces -- to Group Actions on Trees -- Laminations, Foliations, and Trees -- Rips Theory -- Brooks’ Theorem and Circle Packings -- Pleated Surfaces and Ends of Hyperbolic Manifolds -- Outline of the Proof of the Hyperbolization Theorem -- Reduction to the Bounded Image Theorem -- The Bounded Image Theorem -- Hyperbolization of Fibrations -- The Orbifold Trick -- Beyond the Hyperbolization Theorem
Dimensions
unknown
Edition
1st ed. 2010.
Extent
1 online resource (485 p.)
Form of item
online
Isbn
9780817649135
Media category
computer
Media type code
c
Other control number
10.1007/978-0-8176-4913-5
Specific material designation
remote
System control number
  • (CKB)1000000000784871
  • (EBL)478175
  • (OCoLC)458558738
  • (SSID)ssj0000175584
  • (PQKBManifestationID)11170377
  • (PQKBTitleCode)TC0000175584
  • (PQKBWorkID)10189566
  • (PQKB)11327180
  • (DE-He213)978-0-8176-4913-5
  • (MiAaPQ)EBC478175
  • (EXLCZ)991000000000784871
Label
Hyperbolic Manifolds and Discrete Groups, by Michael Kapovich, (electronic resource)
Publication
Note
Description based upon print version of record
Bibliography note
Includes bibliographical references and index
Carrier category
online resource
Carrier category code
cr
Content category
text
Content type code
txt
Contents
Three-Dimensional Topology -- Thurston Norm -- Geometry of Hyperbolic Space -- Kleinian Groups -- Teichmüller Theory of Riemann Surfaces -- to Orbifold Theory -- Complex Projective Structures -- Sociology of Kleinian Groups -- Ultralimits of Metric Spaces -- to Group Actions on Trees -- Laminations, Foliations, and Trees -- Rips Theory -- Brooks’ Theorem and Circle Packings -- Pleated Surfaces and Ends of Hyperbolic Manifolds -- Outline of the Proof of the Hyperbolization Theorem -- Reduction to the Bounded Image Theorem -- The Bounded Image Theorem -- Hyperbolization of Fibrations -- The Orbifold Trick -- Beyond the Hyperbolization Theorem
Dimensions
unknown
Edition
1st ed. 2010.
Extent
1 online resource (485 p.)
Form of item
online
Isbn
9780817649135
Media category
computer
Media type code
c
Other control number
10.1007/978-0-8176-4913-5
Specific material designation
remote
System control number
  • (CKB)1000000000784871
  • (EBL)478175
  • (OCoLC)458558738
  • (SSID)ssj0000175584
  • (PQKBManifestationID)11170377
  • (PQKBTitleCode)TC0000175584
  • (PQKBWorkID)10189566
  • (PQKB)11327180
  • (DE-He213)978-0-8176-4913-5
  • (MiAaPQ)EBC478175
  • (EXLCZ)991000000000784871

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