Skip to main content

Finiteness Properties of \(\mathbf{G}(\mathbb{F}_{q}[t])\)

  • Chapter
  • First Online:
Finiteness Properties of Arithmetic Groups Acting on Twin Buildings

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 2109))

  • 686 Accesses

Abstract

It is a common situation to have a group G that acts on a polyhedral complex X with the properties that X is contractible and the stabilizers of cells are finite but X is not compact modulo the action of G. One is then interested in a G-invariant subspace X 0 of X that is compact modulo G and still has some desirable properties, in our case to be highly connected.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 49.99
Price excludes VAT (USA)
  • Compact, lightweight 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

Institutional subscriptions

References

  1. Abramenko, P., Brown, K.S.: Buildings: Theory and Applications. Graduate Texts in Mathematics, vol. 248. Springer, New York (2008)

    Google Scholar 

  2. Abramenko, P.: Twin Buildings and Applications to S-Arithmetic Groups. Lecture Notes in Mathematics, vol. 1641. Springer, New York (1996)

    Google Scholar 

  3. Behr, H.: Zur starken approximation in algebraischen Gruppen über globalen Körpern. J. Reine Angew. Math. 229, 107–116 (1968)

    MATH  MathSciNet  Google Scholar 

  4. Bux, K.U., Köhl, R., Witzel, S.: Higher finiteness properties of reductive arithmetic groups in positive characteristic: The Rank Theorem. Ann. Math. (2) 177, 311–366 (2013)

    Google Scholar 

  5. Borel, A., Tits, J.: Compléments à l’article “groupes réductifs”. Inst. Hautes Études Sci. Publ. Math. 41, 253–276 (1972)

    Article  MATH  MathSciNet  Google Scholar 

  6. Bux, K.U., Wortman, K.: Connectivity properties of horospheres in Euclidean buildings and applications to finiteness properties of discrete groups. Invent. Math. 185, 395–419 (2011)

    Article  MATH  MathSciNet  Google Scholar 

  7. Hatcher, A.: Algebraic Topology. Cambridge University Press, Cambridge (2001)

    Google Scholar 

  8. McMullen, P.: On zonotopes. Trans. Am. Math. Soc. 159, 91–109 (1971)

    Article  MATH  MathSciNet  Google Scholar 

  9. Schulz, B.: Spherical subcomplexes of spherical buildings. Geom. Topol. 17, 531–562 (2013)

    Article  MATH  MathSciNet  Google Scholar 

  10. von Heydebreck, A.: Homotopy properties of certain subcomplexes associated to spherical buildings. Isr. J. Math. 133, 369–379 (2003)

    Article  MATH  Google Scholar 

  11. Ziegler, G.M.: Lectures on Polytopes. Graduate Texts in Mathematics, vol. 152. Springer, Heidelberg (1995)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

Copyright information

© 2014 Springer International Publishing Switzerland

About this chapter

Cite this chapter

Witzel, S. (2014). Finiteness Properties of \(\mathbf{G}(\mathbb{F}_{q}[t])\) . In: Finiteness Properties of Arithmetic Groups Acting on Twin Buildings. Lecture Notes in Mathematics, vol 2109. Springer, Cham. https://doi.org/10.1007/978-3-319-06477-2_2

Download citation

Publish with us

Policies and ethics