Translation Planes [electronic resource] : Foundations and Construction Principles / by Norbert Knarr.

Foundations -- Spreads of 3-dimensional projective spaces -- Kinematic spaces -- Examples and supplements -- Locally compact 4-dimensional translation planes -- Planes of Lenz type V with complex kernel -- Locally compact translation planes of higher dimension.

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.