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The Geometry of Discrete Groups (Paperback, Softcover reprint of the original 1st ed. 1983)
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The Geometry of Discrete Groups (Paperback, Softcover reprint of the original 1st ed. 1983)
Series: Graduate Texts in Mathematics, 91
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Total price: R1,867
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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.
General
Imprint: |
Springer-Verlag New York
|
Country of origin: |
United States |
Series: |
Graduate Texts in Mathematics, 91 |
Release date: |
October 2012 |
First published: |
1983 |
Authors: |
Alan F. Beardon
|
Dimensions: |
235 x 155 x 18mm (L x W x T) |
Format: |
Paperback
|
Pages: |
340 |
Edition: |
Softcover reprint of the original 1st ed. 1983 |
ISBN-13: |
978-1-4612-7022-5 |
Categories: |
Books >
Science & Mathematics >
Mathematics >
Algebra >
Groups & group theory
|
LSN: |
1-4612-7022-7 |
Barcode: |
9781461270225 |
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