Translation Planes: Foundations and Construction Principles

Norbert Knarr (auth.)3540602089, 9783540602088

The book discusses various construction principles for translation planes and spreads from a general and unifying point of view and relates them to the theory of kinematic spaces. The book is intended for people working in the field of incidence geometry and can be read by everyone who knows the basic facts about projective and affine planes.
The methods developed work especially well for topological spreads of real and complex vector spaces. In particular, a complete classification of all semifield spreads of finite dimensional complex vector spaces is obtained.

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Table of contents :
Introduction….Pages 1-4
Foundations….Pages 5-24
Spreads of 3-dimensional projective spaces….Pages 25-39
Kinematic spaces….Pages 40-47
Examples and supplements….Pages 48-60
Locally compact 4-dimensional translation planes….Pages 61-77
Planes of Lenz type V with complex kernel….Pages 78-94
Locally compact translation planes of higher dimension….Pages 95-103