On geometric flats in the CAT(O) realization of coxeter groups and tits buildings

Canadian Journal of Mathematics

Volumn 61, Issue 4, 2009, Pages 740-761

  Caprace, Pierre Emmanue ^a   Frédéric, Haglund ^b  

^a UNIVERSITÉ LIBRE DE BRUXELLES   (Belgium)

^b UNIVERSITÉ PARIS SACLAY   (France)

Author keywords

Building; CAT(O) space; Coxeter group; Flat rank

Indexed keywords

EID: 68849086144     PISSN: 0008414X     EISSN: None     Source Type: Journal    
DOI: 10.4153/CJM-2009-040-8     Document Type: Article

References (20)

1. B. Brink and R. B. Hewlett, A finiteness property and an automatic structure for Coxeter groups. Math. Ann. 296(1993), no.1, 179-190.
2. M. R. Bridson and A. Haefliger, Metric spaces of non-positive curvature. Grundlehren der Mathematischen Wissenschaften 319, Springer-Verlag, Berlin, 1999.
3. U. Baumgartner, B. Remy, and G. A. Willis, Flat rank of automorphism groups of buildings. Transform. Groups 12(2007), no.3,413-436.
4. R-E. Caprace, Conjugacy of 2-spherical subgroups of Coxeter groups and parallel walls. Algebr. Geom. Topol. 6(2006), 1987-2029.
5. R-E. Caprace and B. Muhlherr, Reflection triangles in Coxeter groups and biautomaticity. J. Group Theory, 8(2005), no.4,467-489.
6. M. Davis, Buildings are CAT(0). In: Geometry and Cohomology in Group Theory. London Math. Soc. Lecture Note Ser. 252, Cambridge, 1998. Cambridge University Press, 1988, pp. 108-123.
7. V. V. Deodhar, A note on subgroups generated by reflections in Coxeter groups. Arch. Math. (Basel), 53(1989), no.6, 543-546.
8. M. Gromov, Asymptotic invariants of infinite groups. In: Geometric Group Theory. London Math. Soc. Lecture Note Ser. 182, Cambridge, Cambridge University Press, 1993, pp. 1-295.
9. F. Haglund and F. Paulin, Simplicity de groupes d'automorphismes d'espaces a courbure negative. In: The Epstein birthday schrift. Geom. Topol. Monogr. 1. Geom. Topol. Publ., 1988, pp. 181-248.
10. F. Haglund and D. Wise, Special cube complexes. Geom. Funct. Anal. 17(2008, no. 5, 1551-1620.
11. J. E. Humphreys, Reflection Groups and Coxeter Groups. Cambridge Studies in Advanced Mathematics 29. Cambridge University Press, Cambridge, 1990.
12. M. Kapovich and B. Kleiner, The weak hyperbolization conjecture for 3-dimensional CAT(O) groups. Groups Geom. Dyn. 1(2007), no.1, 61-79.
13. B. Kleiner, The local structure of length spaces with curvature bounded above. Math. Z. 231(1999), no.3,409-456.
14. [Kra94] D. Krammer, The Conjugacy Problem for Coxeter Groups. Ph.D. thesis, Universiteit Utrecht, 1994. http://www.maths.warwick.ac.uk/\%7Edaan/ index.files/Proefschrift12.dvi.
15. G. A. Niblo and L. D. Reeves, Coxeter groups acton CAT(O) cube complexes. J. Group Theory 6(2003), no.3, 399-1113
16. G. Noskov and E. Vinberg, Strong Tits alternative for subgroups of Coxeter groups. J. Lie Theory 12(2002), no.1,259-264.
17. B. Rémy, Topological simplicity, commensurator super-rigidity and non linearity of Kac-Moody groups. With an appendix by P. Bonvin. Geom. Funct. Anal. 14(2004), no.4, 810-852. (Pubitemid 39332473)
18. M. Ronan, Lectures on Buildings. Perspectives in Mathematics 7. Academic Press, Boston, 1989.
19. J Tits, A local approach to buildings. In: The Geometric Vein. Springer, New York, 1981, pp. 519-547.
20. D. T. Wise, Approximating flats by periodic flats in CAT(0) square complexes. Canad. J. Math. 57(2005), no.2,416-448. (Pubitemid 40507184)