Skip to main content

Totally Disconnected, Locally Compact Groups as Geometric Objects

A survey of work in progress

  • Conference paper
Geometric Group Theory

Part of the book series: Trends in Mathematics ((TM))

Abstract

This survey outlines a geometric approach to the structure theory of totally disconnected, locally compact groups. The content of my talk at Geneva is contained in Section 3.

This article originates from the Geneva conference.

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 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 109.99
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

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Martin Bridson and André Haeflinger. Metric Spaces of non-positive Curvature, volume 319 of Grundlehren der mathematischen Wissenschaften. Springer Verlag, 1999.

    Google Scholar 

  2. Udo Baumgartner, Rögnvaldur G. Möller, and George A. Willis. Groups of flat rank at most 1. preprint, 2004.

    Google Scholar 

  3. M. Bourdon. Immeubles hyperboliques, dimension conforme et rigidité de Mostow. Geom. Funct. Anal., 7:245–268, 1997.

    Article  MATH  MathSciNet  Google Scholar 

  4. Udo Baumgartner, Bertrand RĂ©my, and George A. Willis. Flat rank of automorphism groups of buildings. Preprint, available at http://arxiv.org/abs/math.GR/0510290, 2005. To appear in Transformation Groups.

    Google Scholar 

  5. Udo Baumgartner and George A. Willis. Contraction groups and scales of automorphisms of totally disconnected locally compact groups. Israel J. Math., 142:221–248, 2004.

    MATH  MathSciNet  Google Scholar 

  6. Udo Baumgartner and George A. Willis. The direction of an automorphism of a totally disconnected locally compact group. Math. Z., 252:393–428, 2006.

    Article  MATH  MathSciNet  Google Scholar 

  7. Pierre-Emmanuel Caprace and Frédéric Haglund. On geometric flats in the CAT(0) realization of Coxeter groups and Tits buildings. Available at http://www.arxiv.org/abs/math.GR/0607741.

    Google Scholar 

  8. M. Gromov. Asymptotic invariants of infinite groups. In Geometric group theory, Vol. 2 (Sussex, 1991), volume 182 of London Math. Soc. Lecture Note Ser., pages 1–295. Cambridge Univ. Press, Cambridge, 1993.

    Google Scholar 

  9. Edwin Hewitt and Kenneth A. Ross. Abstract Harmonic Analysis; Volume I, volume 115 of Grundlehren der mathematischen Wissenschaften. Springer Verlag, second edition, 1979.

    Google Scholar 

  10. Bruce Kleiner. The local structure of length spaces with curvature bounded above. Math. Z., 231(3):409–456, 1999.

    Article  MATH  MathSciNet  Google Scholar 

  11. Daan Krammer. The conjugacy problem for Coxeter groups. PhD thesis, Universiteit Utrecht, Faculteit Wiskunde & Informatica, 1994.

    Google Scholar 

  12. Rögnvaldur G. Möller. Structure theory of totally disconnected locally compact groups via graphs and permutations. Canadian Journal of Mathematics, 54:795–827, 2002.

    MATH  Google Scholar 

  13. Bertrand Rémy and Mark Ronan. Topological groups of Kac-Moody type, right-angled twinnings and their lattices. Comment. Math. Helv., 81(1):191–219, 2006.

    MATH  MathSciNet  Google Scholar 

  14. George A. Willis. The structure of totally disconnected locally compact groups. Math. Ann., 300:341–363, 1994.

    Article  MATH  MathSciNet  Google Scholar 

  15. George A. Willis. Further properties of the scale function on a totally disconnected locally compact group. J. Algebra, 237:142–164, 2001.

    Article  MATH  MathSciNet  Google Scholar 

  16. George A. Willis. Tidy subgroups for commuting automorphisms of totally disconnected locally compact groups: An analogue of simultaneous triangularisation of matrices. New York Journal of Mathematics, 10:1–35, 2004. available at http://nyjm.albany.edu:8000/j/2004/Vol10.htm.

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2007 Birkhäuser Verlag Basel/Switzerland

About this paper

Cite this paper

Baumgartner, U. (2007). Totally Disconnected, Locally Compact Groups as Geometric Objects. In: Arzhantseva, G.N., Burillo, J., Bartholdi, L., Ventura, E. (eds) Geometric Group Theory. Trends in Mathematics. Birkhäuser Basel. https://doi.org/10.1007/978-3-7643-8412-8_1

Download citation

Publish with us

Policies and ethics