A characterization of higher rank symmetric spaces via bounded cohomology

Geometric and Functional Analysis

Volumn 19, Issue 1, 2009, Pages 11-40

  Bestvina, Mladen ^a   Fujiwara, Koji ^b  

^a UNIVERSITY OF UTAH   (United States)

^b TOHOKU UNIVERSITY   (Japan)

Author keywords

Bounded cohomology; Higher rank symmetric spaces; Quasi homomorphisms; Rank 1 isometries; Rank Rigidity theorem

Indexed keywords

EID: 67650284982     PISSN: 1016443X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00039-009-0717-8     Document Type: Article

References (18)

1. W. BALLMANN, with an appendix by M. BRIN Lectures on Spaces of Nonpositive Curvature, DMV Seminar 25, Birkhäuser Verlag, Basel, 1995.
2. W. BALLMANN, M. BRIN, Orbihedra of nonpositive curvature, Inst. Hautes Études Sci. Publ. Math. 82:1995 (1996), 169-209.
3. W. BALLMANN, P. EBERLEIN, Fundamental groups of manifolds of non-positive curvature, J. Differential Geom. 25:1 (1987), 1-22.
4. C. BAVARD, Longueur stable des commutateurs, Enseign. Math. (2) 37:1-2 (1991), 109-150.
5. J.A. BEHRSTOCK, Asymptotic geometry of the mapping class group and Teichmüller space, Geom. Topol. 10 (2006), 1523-1578.
6. M. BESTVINA, K. FUJIWARA, Bounded cohomology of subgroups of mapping class groups, Geom. Topol. 6 (2002), 69-89.
7. R. BROOKS, Some remarks on bounded cohomology, in "Riemann Surfaces and Related Topics: Proceedings of the 1978 Stony Brook Conference (State Univ. New York, Stony Brook, N.Y., 1978)", Ann. of Math. Stud. 797, Princeton University Press, Princeton, NJ, (1981), 53-63.
8. M. BURGER, N. MONOD, Bounded cohomology of lattices in higher rank Lie groups, J. Eur. Math. Soc. (JEMS) 1:2 (1999), 199-235.
9. M. BURGER, N. MONOD, Continuous bounded cohomology and applications to rigidity theory, GAFA, Geom. funct. anal. 12:2 (2002), 219-280.
10. R.D. CANARY, Ends of hyperbolic 3-manifolds, J. Amer. Math. Soc. 6:1 (1993), 1-35.
11. P.-E. CAPRACE, K. FUJIWARA, Rank one isometries of buildings and quasi-morphisms of Kac-Moody groups, GAFA, Geom. funct. anal., to appear.
12. P.B. EBERLEIN, Geometry of Nonpositively Curved Manifolds, Chicago Lectures in Mathematics. University of Chicago Press, Chicago, IL, 1996.
13. D.B.A. EPSTEIN, K. FUJIWARA, The second bounded cohomology of word-hyperbolic groups, Topology 36:6 (1997), 1275-1289.
14. K. FUJIWARA, The second bounded cohomology of a group acting on a Gromov-hyperbolic space, Proc. London Math. Soc. (3) 76:1 (1998), 70-94.
15. K. FUJIWARA, The second bounded cohomology of an amalgamated free product of groups, Trans. Amer. Math. Soc. 352:3 (2000), 1113-1129.
16. J.F. MANNING, with an appendix by N. MONOD, B. RÉMY. Quasi-actions on trees and property (QFA), J. London Math. Soc. (2) 73:1 (2006), 84-108.
17. S.A. WOLPERT, Geometry of the Weil-Petersson completion of Teichmüller space, in "Surveys in Differential Geometry VIII (Boston, MA, 2002)", Surv. Differ. Geom. VIII, Int. Press, Somerville, MA (2003), 357-393.
18. DONGPING ZHUANG, Irrational stable commutator length in finitely pre-sented groups, J. Mod. Dyn. 2:3 (2008), 499-507.