Skip to main content

Chamber Systems

  • Chapter
  • 1484 Accesses

Abstract

The study of geometries can be developed starting from a different viewpoint than the diagram geometric one of the previous chapter. It corresponds to the structure induced on the set of maximal flags, also called chambers (cf. Definition 1.2.5), of a geometry. This slightly more abstract viewpoint has advantages for the study of thin geometries as well as group-related geometries.

This is a preview of subscription content, log in via an institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   89.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   149.00
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD   119.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

References

  1. M.R. Bridson, A. Haefliger, Metric Spaces of Non-positive Curvature. Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 319 (Springer, Berlin, 1999)

    MATH  Google Scholar 

  2. F. Buekenhout, An introduction to incidence geometry, in Handbook of Incidence Geometry (North-Holland, Amsterdam, 1995), pp. 1–25

    Chapter  Google Scholar 

  3. R. Gramlich, H. van Maldeghem, Intransitive geometries. Proc. Lond. Math. Soc. (3) 93, 666–692 (2006)

    Article  MATH  Google Scholar 

  4. T. Meixner, F. Timmesfeld, Chamber systems with string diagrams. Geom. Dedic. 15, 115–123 (1983)

    Article  MathSciNet  MATH  Google Scholar 

  5. A. Pasini, Diagram Geometries. Oxford Science Publications (Clarendon/Oxford University Press, New York, 1994)

    MATH  Google Scholar 

  6. J. Tits, A local approach to buildings, in The Geometric Vein (Springer, New York, 1981), pp. 519–547

    Chapter  Google Scholar 

  7. J. Tits, Buildings and group amalgamations, in Proceedings of Groups—St. Andrews 1985. London Math. Soc. Lecture Note Ser., vol. 121 (Cambridge University Press, Cambridge, 1986), pp. 110–127

    Google Scholar 

  8. J. Tits, Ensembles ordonnés, immeubles et sommes amalgamées. Bull. Soc. Math. Belg., Sér. A 38, 367–387 (1986)

    MathSciNet  MATH  Google Scholar 

  9. P.-H. Zieschang, An Algebraic Approach to Association Schemes. Lecture Notes in Mathematics, vol. 1628 (Springer, Berlin, 1996)

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

Copyright information

© 2013 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Buekenhout, F., Cohen, A.M. (2013). Chamber Systems. In: Diagram Geometry. Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics, vol 57. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-34453-4_3

Download citation

Publish with us

Policies and ethics