Graduate Texts in Mathematics

The Geometry of Discrete Groups

Authors: Beardon, Alan F.

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About this Textbook

This text is intended to serve as an introduction to the geometry of the action of discrete groups of Mobius transformations. The subject matter has now been studied with changing points of emphasis for over a hundred years, the most recent developments being connected with the theory of 3-manifolds: see, for example, the papers of Poincare [77] and Thurston [101]. About 1940, the now well-known (but virtually unobtainable) Fenchel-Nielsen manuscript appeared. Sadly, the manuscript never appeared in print, and this more modest text attempts to display at least some of the beautiful geo­ metrical ideas to be found in that manuscript, as well as some more recent material. The text has been written with the conviction that geometrical explana­ tions are essential for a full understanding of the material and that however simple a matrix proof might seem, a geometric proof is almost certainly more profitable. Further, wherever possible, results should be stated in a form that is invariant under conjugation, thus making the intrinsic nature of the result more apparent. Despite the fact that the subject matter is concerned with groups of isometries of hyperbolic geometry, many publications rely on Euclidean estimates and geometry. However, the recent developments have again emphasized the need for hyperbolic geometry, and I have included a comprehensive chapter on analytical (not axiomatic) hyperbolic geometry. It is hoped that this chapter will serve as a "dictionary" offormulae in plane hyperbolic geometry and as such will be of interest and use in its own right.

Table of contents (11 chapters)

Buy this book

eBook $69.99
price for USA (gross)
  • ISBN 978-1-4612-1146-4
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $89.95
price for USA
  • ISBN 978-0-387-90788-8
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $89.95
price for USA
  • ISBN 978-1-4612-7022-5
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
The Geometry of Discrete Groups
Authors
Series Title
Graduate Texts in Mathematics
Series Volume
91
Copyright
1983
Publisher
Springer-Verlag New York
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-1-4612-1146-4
DOI
10.1007/978-1-4612-1146-4
Hardcover ISBN
978-0-387-90788-8
Softcover ISBN
978-1-4612-7022-5
Series ISSN
0072-5285
Edition Number
1
Number of Pages
XII, 340
Topics