Bounded Kähler class rigidity of actions on hermitian symmetric spaces

Marc Burger; Alessandra Iozzi

Annales scientifiques de l'École Normale Supérieure (2004)

  • Volume: 37, Issue: 1, page 77-103
  • ISSN: 0012-9593

How to cite


Burger, Marc, and Iozzi, Alessandra. "Bounded Kähler class rigidity of actions on hermitian symmetric spaces." Annales scientifiques de l'École Normale Supérieure 37.1 (2004): 77-103. <>.

author = {Burger, Marc, Iozzi, Alessandra},
journal = {Annales scientifiques de l'École Normale Supérieure},
keywords = {bounded Kähler class; rigidity; Hermitian symmetric space},
language = {eng},
number = {1},
pages = {77-103},
publisher = {Elsevier},
title = {Bounded Kähler class rigidity of actions on hermitian symmetric spaces},
url = {},
volume = {37},
year = {2004},

AU - Burger, Marc
AU - Iozzi, Alessandra
TI - Bounded Kähler class rigidity of actions on hermitian symmetric spaces
JO - Annales scientifiques de l'École Normale Supérieure
PY - 2004
PB - Elsevier
VL - 37
IS - 1
SP - 77
EP - 103
LA - eng
KW - bounded Kähler class; rigidity; Hermitian symmetric space
UR -
ER -


  1. [1] A'Campo N., Burger M., Réseaux arithmétiques et commensurateurs d'après G. A. Margulis, Invent. Math.116 (1994) 1-25. Zbl0833.22014MR1253187
  2. [2] Benoist Y., Actions propres sur les espaces homogènes réductifs, Ann. of Math. (2)144 (1996) 315-347. Zbl0868.22013MR1418901
  3. [3] Benoist Y., Labourie F., Sur les difféomorphismes d'Anosov affines à feuilletages stable et instable différentiables, Invent. Math.111 (1993) 285-308. Zbl0777.58029MR1198811
  4. [4] Bradlow S.B., Garcia-Prada O., Gothen P.B., Surface group representations in PU(p,q) and Higgs bundles, Zbl1070.53054MR2123494
  5. [5] Brooks R., Some remarks on bounded cohomology, in: Riemann Surfaces and Related Topics: Proceedings of the 1978 Stony Brook Conference (State Univ. New York, Stony Brook, NY, 1978) (Princeton, NJ), Ann. of Math. Stud., vol. 97, Princeton Univ. Press, 1981, pp. 53-63. Zbl0457.55002MR624804
  6. [6] Burger M., Iozzi A., Boundary maps in bounded cohomology, Geom. Funct. Anal.12 (2002) 281-292. Zbl1006.22011MR1911668
  7. [7] Burger M., Iozzi A., Wienhard A., Surface group representations with maximal Toledo invariant, C. R. Acad. Sci. Paris Sér. I336 (2003) 387-390. Zbl1035.32013MR1979350
  8. [8] Burger M., Monod N., Continuous bounded cohomology and applications, unpublished. Zbl1006.22010
  9. [9] Burger M., Monod N., Continuous bounded cohomology and applications to rigidity theory, Geom. Funct. Anal.12 (2002) 219-280. Zbl1006.22010MR1911660
  10. [10] Clerc J.L., Ørsted B., The Gromov norm of the Käehler class and the Maslov index, preprint, June 2002. 
  11. [11] Domic A., Toledo D., The Gromov norm of the Käehler class of symmetric domains, Math. Ann.276 (3) (1987) 425-432. Zbl0595.53061MR875338
  12. [12] Dupont J.L., Bounds for Characteristic Numbers of Flat Bundles, in: Algebraic topology, Aarhus 1978, Lecture Notes in Mathematics, vol. 763, Springer-Verlag, 1979. Zbl0511.57018MR561216
  13. [13] Dupont J.L., Guichardet A., À propos de l'article: “Sur la cohomologie réelle des groupes de Lie simples réels”, Ann. Sci. École Norm. Sup. (4)11 (2) (1978) 277-292, par A. Guichardet et D. Wigner , Ann. Sci. École Norm. Sup. (4)11 (2) (1978) 293-295. Zbl0398.22016
  14. [14] Ghys É., Groupes d'homéomorphismes du cercle et cohomologie bornée, in: The Lefschetz Centennial Conference, Part III (Mexico City 1984), Contemp. Math., vol. 58, American Mathematical Society, RI, 1987, pp. 81-106. Zbl0617.58009MR893858
  15. [15] Ghys É., Le cercle à l'infini des surfaces à courbure négative, in: Proceedings of the International Congress of Mathematicians, vols. I, II (Kyoto, 1990) (Tokyo), Math. Soc. Japan, 1991, pp. 501-509. Zbl0747.53032MR1159237
  16. [16] Goldman W.M., Complex Hyperbolic Geometry, Oxford Mathematical Monographs, The Clarendon Press Oxford University Press, New York, 1999, Oxford Science Publications. Zbl0939.32024MR1695450
  17. [17] Goldman W.M., Topological components of spaces of representations, Invent. Math.93 (3) (1988) 557-607. Zbl0655.57019MR952283
  18. [18] Grigorchuk R.I., Some results on bounded cohomology, in: Combinatorial and Geometric Group Theory (Edinburgh, 1993), London Math. Soc. Lecture Note Ser., vol. 204, Cambridge Univ. Press, Cambridge, 1995, pp. 111-163. Zbl0853.20034MR1320279
  19. [19] Guichardet A., Wigner D., Sur la cohomologie réelle des groupes de Lie simples réels, Ann. Sci. École Norm. Sup. (4)11 (2) (1978) 277-292. Zbl0398.22015MR510552
  20. [20] Gusevskii N., Parker J.R., Representations of free Fuchsian groups in complex hyperbolic space, Topology39 (2000) 33-60. Zbl0977.32017MR1710991
  21. [21] Hernàndez Lamoneda L., Maximal representations of surface groups in bounded symmetric domains, Trans. Amer. Math. Soc.324 (1991) 405-420. Zbl0733.32024MR1033234
  22. [22] Iozzi A., Bounded cohomology, boundary maps, and representations into Homeo+(S1) and SU(1,n), in: Rigidity in Dynamics and Geometry, Cambridge, UK, 2000, Springer-Verlag, 2002, pp. 237-260. Zbl1012.22023MR1919404
  23. [23] Kaimanovich V.A., The Poisson boundary of an amenable extension, Monatsh. Math.136 (1) (2002) 9-15. Zbl1004.43001MR1908077
  24. [24] Margulis G.A., Discrete Subgroups of Semisimple Lie Groups, Springer-Verlag, New York, 1991. Zbl0732.22008MR1090825
  25. [25] Matsumoto S., Some remarks on foliated S1 bundles, Invent. Math.90 (1987) 343-358. Zbl0681.58007MR910205
  26. [26] Mitsumatsu Y., Bounded cohomology and l1-homology of surfaces, Topology23 (4) (1984) 465-471. Zbl0568.55002MR780736
  27. [27] Monod N., Continuous Bounded Cohomology of Locally Compact Groups, Lecture Notes in Math., vol. 1758, Springer-Verlag, 2001. Zbl0967.22006MR1840942
  28. [28] Monod N., Shalom Y., Rigidity of orbit equivalence and bounded cohomology, Ann. Math., in press. Zbl1129.37003
  29. [29] Prasad G., R-regular elements in Zariski-dense subgroups, Quart. J. Math. Oxford Ser. (2)45 (180) (1994) 541-545. Zbl0828.22010MR1315463
  30. [30] Prasad G., Raghunathan M.S., Cartan subgroups and lattices in semi-simple groups, Ann. of Math.96 (1972) 296-317. Zbl0245.22013MR302822
  31. [31] Procesi C., Schwarz G., Inequalities defining orbit spaces, Invent. Math.81 (3) (1985) 539-554. Zbl0578.14010MR807071
  32. [32] Toledo D., Harmonic maps from surfaces to certain Kähler manifolds, Math. Scand.45 (1979) 13-26. Zbl0435.58008MR567429
  33. [33] Toledo D., Representations of surface groups in complex hyperbolic space, J. Differential Geom.29 (1) (1989) 125-133. Zbl0676.57012MR978081
  34. [34] Xia E.Z., The moduli of flat U(p,1) structures on Riemann surfaces, preprint, 2001. MR2003688
  35. [35] Zimmer R.J., Amenable ergodic group actions and an application to Poisson boundaries of random walks, J. Funct. Anal.27 (1978) 350-372. Zbl0391.28011MR473096

NotesEmbed ?


You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.


Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.