Groups acting on CAT(0) square complexes

Geometriae Dedicata

Volumn 109, Issue 1, 2004, Pages 59-88

  Xie, Xiangdong ^a  

^a WASHINGTON UNIVERSITY   (United States)

Author keywords

CAT(0); Free group; Geodesic; Square complex; Tits metric

Indexed keywords

EID: 23844460872     PISSN: 00465755     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10711-004-1527-7     Document Type: Article

References (27)

1. Adams, S. and Ballmann, W.: Amenable isometry groups of Hadamard spaces, Math. Ann. 312(1) (1998), 183-195.
2. Alperin, R., Farb, B. and Noskov, G.: A strong Schottky lemma for nonpositively curved singular spaces, Geom. Dedicata 92 (2002), 235-243.
3. Ballmann, W.: Lectures on Spaces of Nonpositive Curvature, vol. 25, DMV Seminar, Birkhäuser, Basel, 1995.
4. Ballmann, W. and Buyalo, S.: Periodic rank one geodesics in Hadamard spaces, Preprint, 2002.
5. Ballmann, W. and Brin, M.: Orbihedra of nonpositive curvature, Inst. Hautes Études Sci. Publ. Math. 82 (1996), 169-209.
6. Ballmann, W. and Brin, M.: Polygonal complexes and combinatorial group theory, Geom. Dedicata 50(2) (1994), 165-191.
7. Benakli, N.: Polygonal complexes. I. Combinatorial and geometric properties, J. Pure Appl. Algebra 97(3) (1994), 247-263.
8. Ballmann, W., Gromov M. and Schroeder, V.: Manifolds of Nonpositive Curvature, Progr. in Math., Birkhäuser, Basel, 1985.
9. Bieri, R.: Normal subgroups in duality groups and in groups of cohomological dimension 2, J. Pure Appl. Algebra 7 (1976), 35-52.
10. Bridson, M. and Haefliger, A.: Metric Spaces of Nonpositive Curvature, Grundl. Math. Wiss. 319, Springer-Verlag, Berlin, 1999.
11. Burger, M. and Mozes, S.: Finitely presented simple groups and products of trees, C.R. Acad. Sci. Paris Ser. I Math. 324(7) (1997), 747-752.
12. Buyalo, S. and Schroeder, V.: On the asymptotic geometry of nonpositively curved graph manifolds, Trans. Amer. Math. Soc. 353 (3) (2001), 853-875.
13. Ballmann, W. and Swiatkowski, J.: On Groups acting on nonpositively curved cubical complexes, Enseign. Math. (2) 45(1-2) (1999), 51-81.
14. Croke, C. and Kleiner, B.: The geodesic flow of a nonpositively curved graph manifold, Geom. Funct. Anal. 12(13) (2002), 479-545.
15. Gromov, M.: Hyperbolic groups, In: S. Gersten (ed.), Essays in Group Theory, MSRI Publ. 8, Springer-Verlag, New York, 1987, pp. 75-263.
16. Kawamura, K. and Ohtsuka, F. Total excess and Tits metric for piecewise Riemannian 2-manifolds, Topol. Appl. 94 (1999), 173-193.
17. Leeb, B.: A Characterization of Irreducible. Symmetric Spaces and Euclidean Buildings of Higher Rank by Their Asymptotic Geometry, Bonn Math. Publ. 326.
18. Niblo, G. and Reeves, L.: Groups acting on CAT(0) cube complexes, Geom. Topol. 1 (1997), 1-7.
19. Niblo, G. and Reeves, L.: The geometry of cube complexes and the complexity of their fundamental groups, Topology 37(3) (1998), 621-633.
20. Pays, I. and Valette, A.: Sous-groupes libres dans les groupes d'automorphismes d'arbres, Enseign. Math. (2) 37(1-2) (1991), 151-174.
21. Ruane, K.: Dynamics of the Action of a CAT(0) group on the boundary, Geom. Dedicata 84 (2001), 81-99.
22. Stallings, J.: A finitely presented group whose 3-dimensional integral homology is not finitely generated, Amer. J. Math. 85 (1963), 541-543.
23. Swenson, E.: A cut point theorem for CAT(O) groups, J. Differential Geom. 53(2) (1999), 327-358.
24. Tits, J.: Free subgroups in linear groups, J. Algebra 20 (1972), 250-270.
25. Wise, D.: Non-positively curved squared complexes, aperiodic tilings, and non-residually finite groups, PhD Thesis, Princeton University, 1996.
26. Xie, X.: Tits alternative for closed real analytic 4-manifolds of nonpositive curvature, Topol. Appl. 136 (2004), 87-121.
27. Xie, X.: The Tits boundary of a CAT(0) 2-complex, Trans. Amer. Math. Soc. (in press).