The geometry of discrete groups
著者
書誌事項
The geometry of discrete groups
（Graduate texts in mathematics, 91）
Springer, c1983
- : us
- : gw
大学図書館所蔵 件 / 全140件
-
: us410.8//G75//447715100117314,15100144748,15100144755,15100144763,15100144771,00013634456
-
: us410.8/G701/910223038219,
: gw410.8/G701/910084205318, 410.8/G701/910090116936 -
該当する所蔵館はありません
- すべての絞り込み条件を解除する
この図書・雑誌をさがす
注記
"With 93 illustrations"
Bibliography: p. [329]-333
Includes index
内容説明・目次
- 巻冊次
-
: us ISBN 9780387907888
内容説明
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.
目次
1 Preliminary Material.- 2 Matrices.- 3 Moebius Transformations on ?n.- 4 Complex Moebius 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.
- 巻冊次
-
: gw ISBN 9783540907886
内容説明
Describing the geometric theory of discrete groups and the associated tesselations of the underlying space, this work also develops the theory of Mobius transformations in n-dimensional Euclidean space. These transformations are discussed as isometries of hyperbolic space and are then identified with the elementary transformations of complex analysis. A detailed account of analytic hyperbolic trigonometry is given, and this forms the basis of the subsequent analysis of tesselations of the hyperbolic plane. Emphasis is placed on the geometrical aspects of the subject and on the universal constraints which must be satisfied by all tesselations.
「Nielsen BookData」 より