Hyperbolic groups have flat-rank at most 1

Israel Journal of Mathematics

Volumn 190, Issue 1, 2012, Pages 365-388

  Baumgartner, Udo ^a   Möller, Rögnvaldur G ^b   Willis, George A ^c  

^a University of Iceland ^*  (Germany)

^b UNIVERSITY OF ICELAND   (Iceland)

^c UNIVERSITY OF NEWCASTLE   (Australia)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84865573347     PISSN: 00212172     EISSN: 15658511     Source Type: Journal    
DOI: 10.1007/s11856-011-0191-5     Document Type: Article

References (24)

1. H. Abels, Specker-Kompaktifizierungen von lokal kompakten topologischen Gruppen, Mathematische Zeitschrift 135 (1973/74), 325-361.
2. H. Bass, Covering theory for graphs of groups, Journal of pure and applied Algebra 89 (1993), 3-47.
3. U. Baumgartner, Totally disconnected, locally compact groups as geometric objects -a survey of work in progress, in Geometric Group Theory · Geneva and Barcelona Conferences (2005), Trends in Mathematics, Birkhäuser Verlag, Basel, 2007, pp. 1-20.
4. M. Bridson and A. Haeflinger, Metric Spaces of non-positive Curvature, Volume 319 of Grundlehren der Mathematischen Wissenschaften, Springer-Verlag, Berlin, 1999.
5. M. Burger and N. Monod, Continuous bounded cohomology and applications to rigidity theory, Geometric and Functional Analysis 12 (2002), 219-280.
6. U. Baumgartner, B. Rémy, and G. A. Willis, Flat rank of automorphism groups of buildings, Transformation Groups 12 (2007), 413-436.
7. U. Baumgartner, G. Schlichting and G. A. Willis, Geometric characterization of flat groups of automorphisms, Groups, Geometry, and Dynamics 4 (2010), 1-13.
8. U. Baumgartner and G. A. Willis, The direction of an automorphism of a totally disconnected locally compact group, Mathematische Zeitschrift 252 (2006), 393-428.
9. M. Coornaert, T. Delzant, and A. Papadopoulos, Géométrie et théorie des groupes, Volume 1441 of Lecture Notes in Mathematics, Springer-Verlag, Berlin, 1990. Les groupes hyperboliques de Gromov [Gromov hyperbolic groups], With an English summary.
10. P.-E. Caprace and F. Haglund, On geometrical flats in the CAT(0) realization of Coxeter groups and Tits buildings, Canadian Journal of Mathematics 61 (2009), 740-761.
11. Y. Cornulier and R. Tessera, Contracting automorphisms and Lp-cohomology in degree one, Arkiv för Matematik, to appear. Available at http://arxiv.org/abs/0908.2603.
12. A. Eskin, D. Fisher and K. Whyte, Quasi-isometries and rigidity of solvable groups Pure and Applied Mathematics Quarterly 3 (2007), 927-947.
13. É. Ghys and P. de la Harpe(editors), Sur les groupes hyperboliques d'apr'es Mikhael Gromov, Progress in Mathematics 83, Birkhäuser Boston Inc., Boston, MA, 1990. Papers from the Swiss Seminar on Hyperbolic Groups held in Bern, 1988.
14. M. Gromov, Hyperbolic groups, in Essays in Group Theory, Volume 8, Mathematical Sciences Research Institute Publications, Springer, New York, 1987, pp. 75-263.
15. F. Haglund and F. Paulin, Simplicité de groupes d'automorphismes d'espaces à courbure négative, in The Epstein birthday Schrift, Geometry & Topology Monographs, Vol. 1, Geom. Topol. Publ., Coventry, 1998, pp. 181-248 (electronic).
16. B. Krön and R. G. Möller, Analogues of Cayley graphs for topological groups, Mathematische Zeitschrift 258 (2008), 637-675.
17. R. G. Moller, Graphs, permutations and topological groups, in the Proceedings of the 2007 Blaubeuren Workshop, Totally disconnected Groups, Graphs and Geometry, to appear. Available at http://arxiv.org/abs/1008.3062.
18. R. G. Möller, Structure theory of totally disconnected locally compact groups via graphs and permutations, Canadian Journal of Mathematics 54 (2002), 795-827.
19. --elements in totally disconnected groups and automorphisms of infinite graphs, Mathematica Scandinavica 92 (2003), 261-268.
20. N. Monod, Continuous Bounded Cohomology of Locally Compact Groups, Lecture Notes in Mathematics, Vol. 1758, Springer, Berlin, 2001.
21. J. Tits, Sur le groupe d'automorphisme d'un arbre, in Essays on Topology and related topics (Memoires dédiés à Georges de Rham) (André Haeflinger and Raghavan Narisimhan, ed.), Springer Verlag, New York, 1970, pp. 188-211.
22. G. A. Willis, Further properties of the scale function on a totally disconnected locally compact group, Journal of Algebra 237 (2001), 142-164.
23. G. A. Willis, Tidy subgroups for commuting automorphisms of totally disconnected locally compact groups: An analogue of simultanous triangularisation of matrices, New York Journal of Mathematics 10 (2004), 1-35.
24. W. Woess, Fixed sets and free subgroups of groups acting on metric spaces, Mathematische Zeitschrift 214 (1993), 425-440.