Universitext

Lectures on Hyperbolic Geometry

Authors: Benedetti, Riccardo, Petronio, Carlo

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eBook $44.99
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  • ISBN 978-3-642-58158-8
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Softcover $59.95
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  • ISBN 978-3-540-55534-6
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About this Textbook

In recent years hyperbolic geometry has been the object and the preparation for extensive study that has produced important and often amazing results and also opened up new questions. The book concerns the geometry of manifolds and in particular hyperbolic manifolds; its aim is to provide an exposition of some fundamental results, and to be as far as possible self-contained, complete, detailed and unified. Since it starts from the basics and it reaches recent developments of the theory, the book is mainly addressed to graduate-level students approaching research, but it will also be a helpful and ready-to-use tool to the mature researcher. After collecting some classical material about the geometry of the hyperbolic space and the Teichmüller space, the book centers on the two fundamental results: Mostow's rigidity theorem (of which a complete proof is given following Gromov and Thurston) and Margulis' lemma. These results form the basis for the study of the space of the hyperbolic manifolds in all dimensions (Chabauty and geometric topology); a unified exposition is given of Wang's theorem and the Jorgensen-Thurston theory. A large part is devoted to the three-dimensional case: a complete and elementary proof of the hyperbolic surgery theorem is given based on the possibility of representing three manifolds as glued ideal tetrahedra. The last chapter deals with some related ideas and generalizations (bounded cohomology, flat fiber bundles, amenable groups). This is the first book to collect this material together from numerous scattered sources to give a detailed presentation at a unified level accessible to novice readers.

Table of contents (6 chapters)

  • Hyperbolic Space

    Benedetti, Riccardo (et al.)

    Pages 1-43

  • Hyperbolic Manifolds and the Compact Two-dimensional Case

    Benedetti, Riccardo (et al.)

    Pages 45-82

  • The Rigidity Theorem (Compact Case)

    Benedetti, Riccardo (et al.)

    Pages 83-131

  • Margulis’ Lemma and its Applications

    Benedetti, Riccardo (et al.)

    Pages 133-157

  • The Space of Hyperbolic Manifolds and the Volume Function

    Benedetti, Riccardo (et al.)

    Pages 159-272

Buy this book

eBook $44.99
price for USA (gross)
  • ISBN 978-3-642-58158-8
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $59.95
price for USA
  • ISBN 978-3-540-55534-6
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Lectures on Hyperbolic Geometry
Authors
Series Title
Universitext
Copyright
1992
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-642-58158-8
DOI
10.1007/978-3-642-58158-8
Softcover ISBN
978-3-540-55534-6
Series ISSN
0172-5939
Edition Number
1
Number of Pages
XIV, 330
Topics