The Geometry of Discrete Groups

The Geometry of Discrete Groups

1983 | Alan F. Beardon
The provided text is the preface and table of contents for the book "The Geometry of Discrete Groups" by Alan F. Beardon, published by Springer-Verlag Berlin Heidelberg GmbH. The book is part of the Graduate Texts in Mathematics series and is intended as an introduction to the geometry of the action of discrete groups of Möbius transformations. It covers various topics including matrices, Möbius transformations on \(\mathbb{R}^n\), complex Möbius transformations, discontinuous groups, Riemann surfaces, hyperbolic geometry, Fuchsian groups, fundamental domains, and finitely generated groups. The author emphasizes the importance of geometrical explanations and provides detailed proofs to ensure a comprehensive understanding of the material. The book also includes a comprehensive chapter on analytical hyperbolic geometry, which serves as a "dictionary" of formulae in plane hyperbolic geometry. The prerequisites for the book are kept to a minimum, and the content is structured to allow for different perspectives on the same topics.The provided text is the preface and table of contents for the book "The Geometry of Discrete Groups" by Alan F. Beardon, published by Springer-Verlag Berlin Heidelberg GmbH. The book is part of the Graduate Texts in Mathematics series and is intended as an introduction to the geometry of the action of discrete groups of Möbius transformations. It covers various topics including matrices, Möbius transformations on \(\mathbb{R}^n\), complex Möbius transformations, discontinuous groups, Riemann surfaces, hyperbolic geometry, Fuchsian groups, fundamental domains, and finitely generated groups. The author emphasizes the importance of geometrical explanations and provides detailed proofs to ensure a comprehensive understanding of the material. The book also includes a comprehensive chapter on analytical hyperbolic geometry, which serves as a "dictionary" of formulae in plane hyperbolic geometry. The prerequisites for the book are kept to a minimum, and the content is structured to allow for different perspectives on the same topics.
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