Totally disconnected, locally compact groups as geometric objects: A survey of work in progress

Trends in Mathematics

Volumn 40, Issue , 2007, Pages 1-20

  Baumgartner, Udo ^a  

^a UNIVERSITY OF NEWCASTLE   (Australia)

Author keywords

Automorphism group; Contraction group; Eigenfactor; Flat rank; Flat subgroup; Rank of CAT(0) space; Scale function; Space of directions; Tits metric; Totally disconnected group

Indexed keywords

EID: 84959145994     PISSN: 22970215     EISSN: 2297024X     Source Type: Book Series    
DOI: None     Document Type: Conference Paper

References (16)

1. [BH99] Martin Bridson and André Haeflinger. Metric Spaces of non-positive Curvature, volume 319 of Grundlehren der mathematischen Wissenschaften. Springer Verlag, 1999.
2. [BMW04] Udo Baumgartner, Rögnvaldur G. Möller, and George A. Willis. Groups of flat rank at most 1. preprint, 2004.
3. [Bou97] M. Bourdon. Immeubles hyperboliques, dimension conforme et rigidité de Mostow. Geom. Funct. Anal., 7:245-268, 1997.
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.
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.
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.
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.
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.
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.
10. [Kle99] Bruce Kleiner. The local structure of length spaces with curvature bounded above. Math. Z., 231(3):409-456, 1999.
11. [Kra94] Daan Krammer. The conjugacy problem for Coxeter groups. PhD thesis, Universiteit Utrecht, Faculteit Wiskunde & Informatica, 1994.
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.
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.
14. [Wil94] George A. Willis. The structure of totally disconnected locally compact groups. Math. Ann., 300:341-363, 1994.
15. [Wil01] George A. Willis. Further properties of the scale function on a totally disconnected locally compact group. J. Algebra, 237:142-164, 2001.
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.