Points and Lines: Characterizing the Classical Geometries

By Ernest E. Shult

I.Basics.- 1 Basics about Graphs.- 2 .Geometries: Basic Concepts.- 3 .Point-line Geometries.-4.Hyperplanes, Embeddings and Teirlinck's Eheory.- II.The Classical Geometries.- 5 .Projective Planes.-6.Projective Spaces.- 7.Polar Spaces.- 8.Near Polygons.- III.Methodology.- 9.Chamber Systems and Buildings.- 10.2-Covers of Chamber Systems.- 11.Locally Truncated Diagram Geometries.-12.Separated Systems of Singular Spaces.- 13 Cooperstein's Theory of Symplecta and Parapolar Spaces.- IV.Applications to Other Lie Incidence Geometries.- 15.Characterizing the Classical Strong Parapolar Spaces: The Cohen-Cooperstein Theory Revisited.- 16.Characterizing Strong Parapolar Spaces by the Relation between Points and Certain Maximal Singular Subspaces.- 17.Point-line Characterizations of the "Long Root Geometries".- 18.The Peculiar Pentagon Property.

• Format: Paperback
• Language: English
• ISBN: 3642156266
• ISBN13: 9783642156267
• Release Date: December 2010
• Publisher: Springer
• Length: 676 Pages
• Weight: 2.12 lbs.
• Dimensions: 1.4" x 6.1" x 9.2"