Point-Line Geometries

Abstract

Point-line geometries are just rank two geometries, and so inherit the concepts of morphism and cover from the last chapter. The symmetry between the two types is broken by the concept of a subspace, which treats points differently from lines. A new graph, the point-collinearity graph, is useful in describing geometric properties. Singular spaces, partial linear spaces, linear spaces, and gamma spaces, all of which appear among the Lie incidence geometries, are introduced at this point. Of special importance is the notion of a locally connected component of a gamma space. The exercises present a number of classical examples and questions concerning product geometries.