Points and lines : characterizing the classical geometries / Ernest E. Shult - First Edition - xxii, 676 pages : illustrations ; 24 cm. - Universitext .
Includes bibliographical references and index
Basics About Graphs -- Geometries: Basic Concepts -- Point-Line Geometries -- Hyperplanes, Embeddings, and Teirlinck’s Theory -- Projective Planes -- Projective Spaces -- Polar Spaces -- Near Polygons -- Chamber Systems and Buildings - 2-Covers of Chamber Systems -- Locally Truncated Diagram Geometries -- Separated Systems of Singular Spaces -- Cooperstein’s Theory of Symplecta and Parapolar Spaces -- Characterizations of the Classical Grassmann Spaces -- Characterizing the Classical Strong Parapolar Spaces: The Cohen–Cooperstein Theory Revisited -- Characterizing Strong Parapolar Spaces by the Relation Between Points and Certain Maximal Singular Subspaces -- Point-Line Characterizations of the “Long Root Geometries” -- The Peculiar Pentagon Property..
The classical geometries of points and lines include not only the projective and polar spaces, but similar truncations of geometries naturally arising from the groups of Lie type. Virtually all of these geometries (or homomorphic images of them) are characterized in this book by simple local axioms on points and lines. Simple point-line characterizations of Lie incidence geometries allow one to recognize Lie incidence geometries and their automorphism groups.
516.02 / S5624p 2011