Points and Lines Characterizing the Classical Geometries

Points and Lines Characterizing the Classical Geometries / by Ernest E. Shult.

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...

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Bibliographic Details
Main Author: Shult, Ernest E. (Author)
Corporate Author: SpringerLink (Online service)
Format: eBook
Language:English
Published: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2011.
Edition:1st ed. 2011.
Series:Universitext,
Springer eBook Collection.
Subjects:
Geometry.
Topological groups.
Lie groups.
Electronic resources (E-books)
Online Access:Click to view e-book
Holy Cross Note:Loaded electronically.
Electronic access restricted to members of the Holy Cross Community.
Table of Contents:
  • 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.

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