Logo - springer
Slogan - springer

Mathematics - Algebra | The Geometry of Discrete Groups

The Geometry of Discrete Groups

Beardon, Alan F.

1983, XII, 340 p.

Available Formats:
eBook
Information

Springer eBooks may be purchased by end-customers only and are sold without copy protection (DRM free). Instead, all eBooks include personalized watermarks. This means you can read the Springer eBooks across numerous devices such as Laptops, eReaders, and tablets.

You can pay for Springer eBooks with Visa, Mastercard, American Express or Paypal.

After the purchase you can directly download the eBook file or read it online in our Springer eBook Reader. Furthermore your eBook will be stored in your MySpringer account. So you can always re-download your eBooks.

 
$69.95

(net) price for USA

ISBN 978-1-4612-1146-4

digitally watermarked, no DRM

Included Format: PDF

download immediately after purchase


learn more about Springer eBooks

add to marked items

Hardcover
Information

Hardcover version

You can pay for Springer Books with Visa, Mastercard, American Express or Paypal.

Standard shipping is free of charge for individual customers.

 
$89.95

(net) price for USA

ISBN 978-0-387-90788-8

free shipping for individuals worldwide

usually dispatched within 3 to 5 business days


add to marked items

Softcover
Information

Softcover (also known as softback) version.

You can pay for Springer Books with Visa, Mastercard, American Express or Paypal.

Standard shipping is free of charge for individual customers.

 
$89.95

(net) price for USA

ISBN 978-1-4612-7022-5

free shipping for individuals worldwide

usually dispatched within 3 to 5 business days


add to marked items

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.

Content Level » Graduate

Keywords » Geometry - Groups

Related subjects » Algebra

Table of contents 

1 Preliminary Material.- 2 Matrices.- 3 Möbius Transformations on ?n.- 4 Complex Möbius Transformations.- 5 Discontinuous Groups.- 6 Riemann Surfaces.- 7 Hyperbolic Geometry.- 8 Fuchsian Groups.- 9 Fundamental Domains.- 10 Finitely Generated Groups.- 11 Universal Constraints on Fuchsian Groups.- References.

Popular Content within this publication 

 

Articles

Read this Book on Springerlink

Services for this book

New Book Alert

Get alerted on new Springer publications in the subject area of Group Theory and Generalizations.