Welcome to CRCPress.com! We have customized the Taylor & Francis India website to host CRC Press titles. Please choose www.TandFIndia.com to get the following benefits:
South Asia Editions of CRC Press titles with INR prices
Multiple options to purchase locally
All CRC Press products available
Your CRC Press login credentials will work on TandFIndia.com
Garland Science Website Announcement
The Garland Science website is no longer available to access and you have been automatically redirected to CRCPress.com.
All instructor resources (*see Exceptions) are now available on our Instructor Hub. Your GarlandScience.com instructor credentials will not grant access to the Hub, but existing and new users may request access here.
The student resources previously accessed via GarlandScience.com are no longer available to existing or new users.
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.
Table of Contents
Introduction Circle Planes Introduction Definitions and Notation Models for Classical Circle Planes Derived Structures Antiregular Quadrangles Introduction Generalized Quadrangles Square Projections The Twisting Number Antiregular Quadrangles Characterization of Antiregular Quadrangles Laguerre Planes and Antiregular Quadrangles Introduction Laguerre Planes Constructed from Antiregular Quadrangles Antiregular Quadrangles Constructed from Laguerre Planes Constructing Topologies on the Lie Geometry Möbius Planes and Antiregular Quadrangles Introduction The Lie Geometry of a Möbius Plane The Lifted Lie Geometry of a Flat Möbius Plane Constructing Topologies on the Lifted Lie Geometry Characterizing Quadrangles Obtained from Flat Möbius Planes Minkowski Planes and Antiregular Quadrangles Introduction The Point Space and Parallel Classes The Circle Space The Other Spaces The Derivation of a Minkowski Plane The Lie Geometry of a Minkowski Plane The Lifted Lie Geometry of a Minkowski Plane The Topology on the Lifted Lie Geometry Characterizing Quadrangles Obtained from Minkowski Planes Relationship of Circle Planes Introduction Sisters of Laguerre Planes Sisters of Möbius Planes Sisters of Minkowski Planes The Problem of Apollonius Introduction The Problem of Apollonius in Laguerre Planes The Problem of Apollonius in Möbius Planes One Point and Two Circles Three Circles The Problem of Apollonius in Minkowski Planes Two Points and One Circle One Point and Two circles Three Circles Index Glossary References
"This book is a must read for anyone interested in incidence geometry and especially anybody interested in topological incidence geometry." -Mathematical Reviews, Issue 97b
We provide complimentary e-inspection copies of primary textbooks to instructors considering our books for course adoption.
Most VitalSource eBooks are available in a reflowable EPUB format which allows you to resize text to suit you and enables other accessibility features. Where the content of the eBook requires a specific layout, or contains maths or other special characters, the eBook will be available in PDF (PBK) format, which cannot be reflowed. For both formats the functionality available will depend on how you access the ebook (via Bookshelf Online in your browser or via the Bookshelf app on your PC or mobile device).
CHOICE – Outstanding Academic Title – Award Winner
CHOICE – 2018 Outstanding Academic Title – Award Winner
Shingo Research and Professional Publication Award Winner
The country you have selected will result in the following:
Product pricing will be adjusted to match the corresponding currency.
The title will be removed from your cart because it is not available in this region.