Tits alternative for closed real analytic 4-manifolds of nonpositive curvature

Topology and its Applications

Volumn 136, Issue 1-3, 2004, Pages 87-121

  Xie, Xiangdong ^a  

^a WASHINGTON UNIVERSITY   (United States)

Author keywords

Hadamard space; Nonpositive curvature; Rank one isometry; Tits alternative; Tits metric

Indexed keywords

EID: 0344082838     PISSN: 01668641     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0166-8641(03)00184-6     Document Type: Article

References (27)

1. Adams S. Ballmann W. Amenable isometry groups of Hadamard spaces Math. Ann. 312 1 1998 183-195
2. Abresch U. Schroeder V. Analytic manifolds of nonpositive curvature in: Besse A.L. (Ed.), Collection SMF séminaires et Congrès, Vol. 1 1996
3. Ballmann W. Lectures on Spaces of Nonpositive Curvature DMV Seminar 25 1995 Birkhäuser Basel
4. W. Ballmann, S. Buyalo, Periodic rank one geodesics in Hadamard spaces, Preprint, 2002
5. Ballmann W. Brin M. Orbihedra of nonpositive curvature Inst. Hautes Études Sci. Publ. Math. 82 1996 169-209
6. Ballmann W. Gromov M. Schroeder V. Manifolds of Nonpositive Curvature Progr. Math. 61 1985 Birkhäuser Basel
7. Bridson M. Haefliger A. Metric Spaces of Nonpositive Curvature Grundlehren 319 1999 Springer Berlin
8. M. Bridson, On the semisimplicity of polyhedral isometries, Proc. Amer. Math. Soc. 127 (7) 2143-2146
9. Ballmann W. Swiatkowski J. On groups acting on nonpositively curved cubical complexes Enseign. Math. (2) 45 1-2 1999 51-81
10. Chen S. Eberlein P. Isometry groups of simply connected manifolds of nonpositive curvature Illinois J. Math. 24 1 1980 73-103
11. Eberlein P. Euclidean de Rham factor of a lattice of nonpositive curvature J. Differential Geom. 18 1983 209-220
12. Eberlein P. Lattices in spaces of nonpositive curvature Ann. of Math. 11 1980 435-476
13. Eberlein P. Geodesic flow in certain manifolds without conjugate points Trans. Amer. Math. Soc. 167 1972 151-170
14. Gromov M. Hyperbolic groups in: Gersten S. (Ed.), Essays in Group Theory MSRI Publications 8 1987 75-263 Springer Berlin
15. Hempel J. 3-Manifolds Ann. of Math. Stud. 86 1976 Princeton University Press Princeton, NJ
16. C. Hruska, K. Ruane, in preparation
17. Hummel C. Schroeder V. Tits geometry associated with 4-dimensional closed real-analytic manifolds of nonpositive curvature J. Differential Geom. 48 1998 531-555
18. Hummel C. Schroeder V. Tits geometry of cocompact real-analytic Hadamard manifolds of dimension 4 Differential Geom. Appl. 11 1999 129-143
19. Kapovich M. Hyperbolic Manifolds and Discrete Groups Progr. Math. 183 2001 Birkhäuser Basel
20. B. Leeb, A characterization of irreducible symmetric spaces and Euclidean buildings of higher rank by their asymptotic geometry, Bonn Mathematical Publications 326
21. Pays I. Valette A. Sous-groupes libres dans les groupes d'automorphismes d'arbres Enseign. Math. (2) 37 1-2 1991 151-174
22. Ruane K. Dynamics of the Action of a CAT(0) group on the boundary Geom. Dedicata 84 2001 81-99
23. Schroeder V. Structure of flat subspaces in low-dimensional manifolds of nonpositive curvature Manuscripta Math. 64 1989 77-105
24. Schroeder V. Codimension one tori in manifolds of nonpositive curvature Geom. Dedicata 33 3 1990 251-263
25. Swenson E. A cut point theorem for CAT(0) groups J. Differential Geom. 53 2 1999 327-358
26. Tits J. Free subgroups in linear groups J. Algebra 20 1972 250-270
27. X. Xie, Groups acting on CAT(0) square complexes, Preprint