Bounded Kähler class rigidity of actions on hermitian symmetric spaces

Burger, Marc; Iozzi, Alessandra

doi:10.1016/j.ansens.2003.09.001

Burger, Marc ; Iozzi, Alessandra

Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 37 (2004) no. 1, pp. 77-103.

MR Zbl | 1 citation dans Numdam

DOI : 10.1016/j.ansens.2003.09.001

@article{ASENS_2004_4_37_1_77_0,
     author = {Burger, Marc and Iozzi, Alessandra},
     title = {Bounded {K\"ahler} class rigidity of actions on hermitian symmetric spaces},
     journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure},
     pages = {77--103},
     publisher = {Elsevier},
     volume = {Ser. 4, 37},
     number = {1},
     year = {2004},
     doi = {10.1016/j.ansens.2003.09.001},
     mrnumber = {2050206},
     zbl = {1061.32016},
     language = {en},
     url = {http://www.numdam.org/articles/10.1016/j.ansens.2003.09.001/}
}

TY  - JOUR
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
SP  - 77
EP  - 103
VL  - 37
IS  - 1
PB  - Elsevier
UR  - http://www.numdam.org/articles/10.1016/j.ansens.2003.09.001/
DO  - 10.1016/j.ansens.2003.09.001
LA  - en
ID  - ASENS_2004_4_37_1_77_0
ER  -

%0 Journal Article
%A Burger, Marc
%A Iozzi, Alessandra
%T Bounded Kähler class rigidity of actions on hermitian symmetric spaces
%J Annales scientifiques de l'École Normale Supérieure
%D 2004
%P 77-103
%V 37
%N 1
%I Elsevier
%U http://www.numdam.org/articles/10.1016/j.ansens.2003.09.001/
%R 10.1016/j.ansens.2003.09.001
%G en
%F ASENS_2004_4_37_1_77_0

Burger, Marc; Iozzi, Alessandra. Bounded Kähler class rigidity of actions on hermitian symmetric spaces. Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 37 (2004) no. 1, pp. 77-103. doi : 10.1016/j.ansens.2003.09.001. http://www.numdam.org/articles/10.1016/j.ansens.2003.09.001/

Bibliographie
Cité par

[1] A'Campo N., Burger M., Réseaux arithmétiques et commensurateurs d'après G. A. Margulis, Invent. Math. 116 (1994) 1-25. | EuDML | MR | Zbl

[2] Benoist Y., Actions propres sur les espaces homogènes réductifs, Ann. of Math. (2) 144 (1996) 315-347. | MR | Zbl

[3] Benoist Y., Labourie F., Sur les difféomorphismes d'Anosov affines à feuilletages stable et instable différentiables, Invent. Math. 111 (1993) 285-308. | EuDML | MR | Zbl

[4] Bradlow S.B., Garcia-Prada O., Gothen P.B., Surface group representations in PU(p,q) and Higgs bundles, http://arxiv.org/abs/math.AG/0211431. | MR

[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. | MR | Zbl

[6] Burger M., Iozzi A., Boundary maps in bounded cohomology, Geom. Funct. Anal. 12 (2002) 281-292. | MR | Zbl

[7] Burger M., Iozzi A., Wienhard A., Surface group representations with maximal Toledo invariant, C. R. Acad. Sci. Paris Sér. I 336 (2003) 387-390. | MR | Zbl

[8] Burger M., Monod N., Continuous bounded cohomology and applications, unpublished.

[9] Burger M., Monod N., Continuous bounded cohomology and applications to rigidity theory, Geom. Funct. Anal. 12 (2002) 219-280. | MR | Zbl

[10] Clerc J.L., Ørsted B., The Gromov norm of the Käehler class and the Maslov index, preprint, June 2002. | Zbl

[11] Domic A., Toledo D., The Gromov norm of the Käehler class of symmetric domains, Math. Ann. 276 (3) (1987) 425-432. | EuDML | MR | Zbl

[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. | MR | Zbl

[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. | EuDML | Numdam | Zbl

[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. | MR | Zbl

[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. | MR | Zbl

[16] Goldman W.M., Complex Hyperbolic Geometry, Oxford Mathematical Monographs, The Clarendon Press Oxford University Press, New York, 1999, Oxford Science Publications. | MR | Zbl

[17] Goldman W.M., Topological components of spaces of representations, Invent. Math. 93 (3) (1988) 557-607. | EuDML | MR | Zbl

[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. | MR | Zbl

[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. | EuDML | Numdam | MR | Zbl

[20] Gusevskii N., Parker J.R., Representations of free Fuchsian groups in complex hyperbolic space, Topology 39 (2000) 33-60. | MR | Zbl

[21] Hernàndez Lamoneda L., Maximal representations of surface groups in bounded symmetric domains, Trans. Amer. Math. Soc. 324 (1991) 405-420. | MR | Zbl

[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. | MR | Zbl

[23] Kaimanovich V.A., The Poisson boundary of an amenable extension, Monatsh. Math. 136 (1) (2002) 9-15. | MR | Zbl

[24] Margulis G.A., Discrete Subgroups of Semisimple Lie Groups, Springer-Verlag, New York, 1991. | MR | Zbl

[25] Matsumoto S., Some remarks on foliated S¹ bundles, Invent. Math. 90 (1987) 343-358. | EuDML | MR | Zbl

[26] Mitsumatsu Y., Bounded cohomology and l¹-homology of surfaces, Topology 23 (4) (1984) 465-471. | MR | Zbl

[27] Monod N., Continuous Bounded Cohomology of Locally Compact Groups, Lecture Notes in Math., vol. 1758, Springer-Verlag, 2001. | MR | Zbl

[28] Monod N., Shalom Y., Rigidity of orbit equivalence and bounded cohomology, Ann. Math., in press. | Zbl

[29] Prasad G., R-regular elements in Zariski-dense subgroups, Quart. J. Math. Oxford Ser. (2) 45 (180) (1994) 541-545. | MR | Zbl

[30] Prasad G., Raghunathan M.S., Cartan subgroups and lattices in semi-simple groups, Ann. of Math. 96 (1972) 296-317. | MR | Zbl

[31] Procesi C., Schwarz G., Inequalities defining orbit spaces, Invent. Math. 81 (3) (1985) 539-554. | EuDML | MR | Zbl

[32] Toledo D., Harmonic maps from surfaces to certain Kähler manifolds, Math. Scand. 45 (1979) 13-26. | EuDML | MR | Zbl

[33] Toledo D., Representations of surface groups in complex hyperbolic space, J. Differential Geom. 29 (1) (1989) 125-133. | MR | Zbl

[34] Xia E.Z., The moduli of flat U(p,1) structures on Riemann surfaces, preprint, 2001. | MR | Zbl

[35] Zimmer R.J., Amenable ergodic group actions and an application to Poisson boundaries of random walks, J. Funct. Anal. 27 (1978) 350-372. | MR | Zbl

Cité par Sources :