Points and Lines

Characterizing the Classical Geometries

Authors:

ISBN: 978-3-642-15626-7 (Print) 978-3-642-15627-4 (Online)

Table of contents (18 chapters)

  1. Front Matter

    Pages i-xxii

  2. Basics

    1. Front Matter

      Pages 1-1

    2. No Access

      Book Chapter

      Pages 3-41

      Basics About Graphs

    3. No Access

      Book Chapter

      Pages 43-58

      Geometries: Basic Concepts

    4. No Access

      Book Chapter

      Pages 59-77

      Point-Line Geometries

    5. No Access

      Book Chapter

      Pages 79-101

      Hyperplanes, Embeddings, and Teirlinck’s Theory

  3. The classical geometries.

    1. Front Matter

      Pages 103-103

    2. No Access

      Book Chapter

      Pages 105-133

      Projective Planes

    3. No Access

      Book Chapter

      Pages 135-165

      Projective Spaces

    4. No Access

      Book Chapter

      Pages 167-249

      Polar Spaces

    5. No Access

      Book Chapter

      Pages 251-287

      Near Polygons

  4. Methodology

    1. Front Matter

      Pages 289-289

    2. No Access

      Book Chapter

      Pages 291-397

      Chamber Systems and Buildings

    3. No Access

      Book Chapter

      Pages 399-413

      2-Covers of Chamber Systems

    4. No Access

      Book Chapter

      Pages 415-440

      Locally Truncated Diagram Geometries

    5. No Access

      Book Chapter

      Pages 441-453

      Separated Systems of Singular Spaces

    6. No Access

      Book Chapter

      Pages 455-494

      Cooperstein’s Theory of Symplecta and Parapolar Spaces

  5. Applications to other Lie incidence geometries.

    1. Front Matter

      Pages 495-495

    2. No Access

      Book Chapter

      Pages 497-526

      Characterizations of the Classical Grassmann Spaces

    3. No Access

      Book Chapter

      Pages 527-552

      Characterizing the Classical Strong Parapolar Spaces: The Cohen–Cooperstein Theory Revisited

    4. No Access

      Book Chapter

      Pages 553-601

      Characterizing Strong Parapolar Spaces by the Relation Between Points and Certain Maximal Singular Subspaces

    5. No Access

      Book Chapter

      Pages 603-626

      Point-Line Characterizations of the “Long Root Geometries”

    6. No Access

      Book Chapter

      Pages 627-663

      The Peculiar Pentagon Property

  6. Back Matter

    Pages 665-676