000			02576 a2200229 4500
003			OSt
005			20241111150402.0
008			241111b |||||||| |||| 00| 0 eng d
020			_a978-1-4612-7022-5
040			_aICTS-TIFR
050			_aQA171 .B364
100			_aAlan Frank Beardon
245			_aThe geometry of discrete groups
260			_bSpringer- Verlag, _aHeidelberg: _c[c1983]
300			_a337 p.
490			_a Graduate Texts in Mathematics _vVol. 91
505			_aCh 1. Preliminary Material Ch 2. Matrices Ch 3. Möbius Transformations on ℝn Ch 4. Complex Möbius Transformations Ch 5. Discontinuous Groups Ch 6. Riemann Surfaces Ch 7. Hyperbolic Geometry Ch 8. Fuchsian Groups Ch 9. Fundamental Domains Ch 10. Finitely Generated Groups Ch 11. Universal Constraints On Fuchsian Groups
520			_aThis 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. --- summary provided by publisher
650			_aMathematics
856			_uhttps://link.springer.com/book/10.1007/978-1-4612-1146-4#toc
942			_2lcc _cBK
999			_c35476 _d35476