Discontinuous Groups of Isometries in the Hyperbolic Plane

1. Auflage 2002
ISBN: 978-3-11-017526-4
Verlag: De Gruyter

Buch, Englisch, Band 29, 364 Seiten, Format (B × H): 160 mm x 236 mm, Gewicht: 800 g

Reihe: De Gruyter Studies in Mathematics

This is an introductory textbook on isometry groups of the hyperbolic plane. Interest in such groups dates back more than 120 years. Examples appear in number theory (modular groups and triangle groups), the theory of elliptic functions, and the theory of linear differential equations in the complex domain (giving rise to the alternative name Fuchsian groups). The current book is based on what became known as the famous Fenchel-Nielsen manuscript. Jakob Nielsen (1890-1959) started this project well before World War II, and his interest arose through his deep investigations on the topology of Riemann surfaces and from the fact that the fundamental group of a surface of genus greater than one is represented by such a discontinuous group. Werner Fenchel (1905-1988) joined the project later and overtook much of the preparation of the manuscript. The present book is special because of its very complete treatment of groups containing reversions and because it avoids the use of matrices to represent Moebius maps. This text is intended for students and researchers in the many areas of mathematics that involve the use of discontinuous groups.

Zielgruppe

Research Mathematicians Graduate Students, Academic Libraries

Autoren/Hrsg.

Fenchel, Werner

Nielsen, Jakob

Schmidt, Asmus L.

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis Elementare Analysis und Allgemeine Begriffe
• Mathematik | Informatik Mathematik Topologie Mengentheoretische Topologie
• Mathematik | Informatik Mathematik Algebra Algebraische Strukturen, Gruppentheorie
• Mathematik | Informatik Mathematik Geometrie Elementare Geometrie: Allgemeines

Über Autor(innen)

Asmus L. Schmidt is Associate Professor at the Institute for Mathematical Sciences of the University of Copenhagen, Denmark.