Topological Circle Planes and Topological Quadrangles

Andreas E Schroth (Abt Fur Topologie, Tu Braunschqeig , Germany)

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English

CRC Press
03 November 1995

Analytic geometry; Algebraic topology

Series: Chapman & Hall/CRC Research Notes in Mathematics Series

This research note presents a complete treatment of the connection between topological circle planes and topological generalized quadrangles. The author uses this connection to provide a better understanding of the relationships between different types of circle planes and to solve a topological version of the problem of Apollonius. Topological Circle Planes and Topological Quadrangles begins with a foundation in classical circle planes and the real symmetric generalized quadrangle and the connection between them. This provides a solid base from which the author offers a more generalized exploration of the topological case. He also compares this treatment to the finite case. Subsequent chapters examine Laguerre, Möbius, and Minkowski planes and their respective relationships to antiregular quadrangles. The author addresses the Lie geometry of each and discuss the relationships of circle planes-the ""sisters"" of Möbius, Laguerre, and Minkowski planes - and concludes by solving a topological version of the problem of Apollonius in Laguerre, Möbius, and Minkowski planes. The treatment offered in this volume offers complete coverage of the topic. The first part of the text is accessible to anyone with a background in analytic geometry, while the second part requires basic knowledge in general and algebraic topology. Researchers interested in geometry-particularly in topological geometry-will find this volume intriguing and informative. Most of the results presented are new and can be applied to various problems in the field of topological circle planes.

Features

By: Andreas E Schroth (Abt Fur Topologie Tu Braunschqeig Germany)
Imprint: CRC Press
Country of Publication: United Kingdom
Volume: 337
Dimensions: Height: 246mm, Width: 174mm, Spine: 11mm
Weight: 299g
ISBN: 9780582288119
ISBN 10: 0582288118
Series: Chapman & Hall/CRC Research Notes in Mathematics Series
Pages: 166
Publication Date: 03 November 1995
Audience: College/higher education , Professional and scholarly , Professional & Vocational , A / AS level , Further / Higher Education
Format: Hardback
Publisher's Status: Active

Reviews for Topological Circle Planes and Topological Quadrangles

This book is a must read for anyone interested in incidence geometry and especially anybody interested in topological incidence geometry. -Mathematical Reviews, Issue 97b