Diagram Geometry

Related to Classical Groups and Buildings

  • Francis Buekenhout
  • Arjeh M. Cohen

Table of contents

  1. Front Matter
    Pages I-XIII
  2. Francis Buekenhout, Arjeh M. Cohen
    Pages 1-48
  3. Francis Buekenhout, Arjeh M. Cohen
    Pages 49-102
  4. Francis Buekenhout, Arjeh M. Cohen
    Pages 103-131
  5. Francis Buekenhout, Arjeh M. Cohen
    Pages 133-200
  6. Francis Buekenhout, Arjeh M. Cohen
    Pages 201-251
  7. Francis Buekenhout, Arjeh M. Cohen
    Pages 253-304
  8. Francis Buekenhout, Arjeh M. Cohen
    Pages 305-368
  9. Francis Buekenhout, Arjeh M. Cohen
    Pages 369-409
  10. Francis Buekenhout, Arjeh M. Cohen
    Pages 411-445
  11. Francis Buekenhout, Arjeh M. Cohen
    Pages 447-497
  12. Francis Buekenhout, Arjeh M. Cohen
    Pages 499-569
  13. Back Matter
    Pages 571-592

About this book

Introduction

This book provides a self-contained introduction to diagram geometry.  Tight connections with group theory are shown. It treats thin geometries (related to Coxeter groups) and thick buildings from a diagrammatic perspective. Projective and affine geometry are main examples.  Polar geometry is motivated by polarities on diagram geometries and the complete classification of those polar geometries whose projective planes are Desarguesian is given. It differs from Tits' comprehensive treatment in that it uses Veldkamp's embeddings.

The book intends to be a basic reference for those who study diagram geometry.  Group theorists will find examples of the use of diagram geometry.  Light on matroid theory is shed from the point of view of geometry with linear diagrams.  Those interested in Coxeter groups and those interested in buildings will find brief but self-contained introductions into these topics from the diagrammatic perspective.  Graph theorists will find many highly regular graphs.

The text is written so graduate students will be able to follow the arguments without needing recourse to further literature.

A strong point of the book is the density of examples.

 

Keywords

Algebras Graphs Groups Incidence Geometry

Authors and affiliations

  • Francis Buekenhout
    • 1
  • Arjeh M. Cohen
    • 2
  1. 1.Dépt. MathematiqueUniversité Libre de BruxellesBruxellesBelgium
  2. 2.Dept. Mathematics & Computer ScienceEindhoven University of TechnologyEindhovenNetherlands

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-34453-4
  • Copyright Information Springer-Verlag Berlin Heidelberg 2013
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-642-34452-7
  • Online ISBN 978-3-642-34453-4
  • Series Print ISSN 0071-1136
  • About this book