Discontinuous Groups of Isometries in the Hyperbolic Plane (De Gruyter Studies in Mathematics) (Hardcover)

~ (Author), Jakob Nielsen (Author), Asmus L. Schmidt (Author) "The following considerations are based on the plane of all complex numbers, this plane being closed as usual by a point at infinity, in other..." (more)
Key Phrases: disjoint modulo, dividing modulo, isometric neighbourhood (more...)

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Product Description

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.

About the Author

Professor Asmus Schmidt (University of Copenhagen) is the editor of this first publication in book form of the Fenchel-Nielsen notes. It is on his initiative that the long and difficult way of getting the original notes into the proper shape ready for publication succeeded.

Product Details

• Hardcover: 364 pages
• Publisher: Walter de Gruyter (December 1, 2002)
• Language: English
• ISBN-10: 3110175266
• ISBN-13: 978-3110175264
• Product Dimensions: 9.6 x 6.9 x 1 inches
• Shipping Weight: 1.6 pounds (View shipping rates and policies)
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• Amazon.com Sales Rank: #2,905,936 in Books (See Bestsellers in Books)