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Totally Disconnected, Locally Compact Groups as Geometric Objects

A survey of work in progress
  • Udo Baumgartner
Part of the Trends in Mathematics book series (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.

Keywords

totally disconnected group automorphism group scale function flat subgroup eigenfactor flat rank rank of CAT(0)-space space of directions Tits metric contraction group 

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References

  1. [BH99]
    Martin Bridson and André Haeflinger. Metric Spaces of non-positive Curvature, volume 319 of Grundlehren der mathematischen Wissenschaften. Springer Verlag, 1999.Google Scholar
  2. [BMW04]
    Udo Baumgartner, Rögnvaldur G. Möller, and George A. Willis. Groups of flat rank at most 1. preprint, 2004.Google Scholar
  3. [Bou97]
    M. Bourdon. Immeubles hyperboliques, dimension conforme et rigidité de Mostow. Geom. Funct. Anal., 7:245–268, 1997.zbMATHCrossRefMathSciNetGoogle Scholar
  4. [BRW05]
    Udo Baumgartner, Bertrand Rémy, 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. [BW04]
    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.zbMATHMathSciNetGoogle Scholar
  6. [BW06]
    Udo Baumgartner and George A. Willis. The direction of an automorphism of a totally disconnected locally compact group. Math. Z., 252:393–428, 2006.zbMATHCrossRefMathSciNetGoogle Scholar
  7. [CH]
    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. [Gro93]
    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. [HR79]
    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. [Kle99]
    Bruce Kleiner. The local structure of length spaces with curvature bounded above. Math. Z., 231(3):409–456, 1999.zbMATHCrossRefMathSciNetGoogle Scholar
  11. [Kra94]
    Daan Krammer. The conjugacy problem for Coxeter groups. PhD thesis, Universiteit Utrecht, Faculteit Wiskunde & Informatica, 1994.Google Scholar
  12. [Möl02]
    Rögnvaldur G. Möller. Structure theory of totally disconnected locally compact groups via graphs and permutations. Canadian Journal of Mathematics, 54:795–827, 2002.zbMATHGoogle Scholar
  13. [RR06]
    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.zbMATHMathSciNetGoogle Scholar
  14. [Wil94]
    George A. Willis. The structure of totally disconnected locally compact groups. Math. Ann., 300:341–363, 1994.zbMATHCrossRefMathSciNetGoogle Scholar
  15. [Wil01]
    George A. Willis. Further properties of the scale function on a totally disconnected locally compact group. J. Algebra, 237:142–164, 2001.zbMATHCrossRefMathSciNetGoogle Scholar
  16. [Wil04]
    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.zbMATHMathSciNetCrossRefGoogle Scholar

Copyright information

© Birkhäuser Verlag Basel/Switzerland 2007

Authors and Affiliations

  • Udo Baumgartner
    • 1
  1. 1.School of Mathematical and Physical SciencesThe University of NewcastleCallaghanAustralia

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