Group Theory/Geometry
Surface group representations with maximal Toledo invariant
[Sur les représentations d'un groupe de surface compacte avec invariant de Toledo maximal]
Comptes Rendus. Mathématique, Tome 336 (2003) no. 5, pp. 387-390.

Nous étudions les représentations d'un groupe de surface compacte sur un espace symétrique hermitien et caractérisons celles avec invariant de Toledo maximal.

We study representations of compact surface groups on Hermitian symmetric spaces and characterize those with maximal Toledo invariant.

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Accepté le :
Publié le :
DOI : 10.1016/S1631-073X(03)00065-7
Burger, Marc 1 ; Iozzi, Alessandra 2 ; Wienhard, Anna 3

1 FIM, ETH Zentrum, CH-8092 Zürich, Switzerland
2 Department of Mathematics, ETH Zentrum, CH-8092 Zürich, Switzerland
3 Mathematisches Institut, Rheinische Friedrich-Wilhelms Universität Bonn, 53115 Bonn, Germany
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     title = {Surface group representations with maximal {Toledo} invariant},
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Burger, Marc; Iozzi, Alessandra; Wienhard, Anna. Surface group representations with maximal Toledo invariant. Comptes Rendus. Mathématique, Tome 336 (2003) no. 5, pp. 387-390. doi : 10.1016/S1631-073X(03)00065-7. http://www.numdam.org/articles/10.1016/S1631-073X(03)00065-7/

[1] Borel, A.; Tits, J. Eléments unipotents et sous-groupes paraboliques de groupes réductifs, I, Invent. Math., Volume 12 (1971), pp. 95-104

[2] S.B. Bradlow, O. Garcia–Prada, P.B. Gothen, Surface group representations, Higgs bundles, and holomorphic triples, Preprint, 2002, | arXiv

[3] Burger, M.; Iozzi, A. Boundary maps in bounded cohomology, Geom. Funct. Anal., Volume 12 (2002), pp. 281-292

[4] M. Burger, A. Iozzi, Bounded Kähler class rigidity of actions on Hermitian symmetric spaces, Preprint, 2002, http://www.math.ethz.ch/~iozzi/supq.ps

[5] Burger, M.; Monod, N. Continuous bounded cohomology and applications to rigidity theory, Geom. Funct. Anal., Volume 12 (2002), pp. 219-280

[6] Clerc, J.L.; Ørsted, B. The Maslov index revisited, Transformation Groups, Volume 6 (2001), pp. 303-320

[7] J.L. Clerc, B. Ørsted, The Gromov norm of the Kähler class and the Maslov index, Preprint, 2002

[8] Domic, A.; Toledo, D. The Gromov norm of the Kähler class of symmetric domains, Math. Ann., Volume 276 (1987), pp. 425-432

[9] W.M. Goldman, Discontinuous groups and the Euler class, Thesis, University of California at Berkeley, 1980

[10] Hernàndez Lamoneda, L. Maximal representations of surface groups in bounded symmetric domains, Trans. Amer. Math. Soc., Volume 324 (1991), pp. 405-420

[11] Ihara, S. Holomorphic imbeddings of symmetric domains, J. Math. Soc. Japan, Volume 19 (1967) no. 3

[12] Iozzi, A. Bounded cohomology, boundary maps, and representations into Homeo+(S1) and SU(1,n), Rigidity in Dynamics and Geometry, Cambridge, UK, 2000, Springer-Verlag, Heidelberg, 2000, pp. 237-260

[13] Monod, N. Continuous bounded cohomology of locally compact groups, Lecture Notes in Math., 1758, Springer-Verlag, Heidelberg, 2001

[14] Satake, I. Holomorphic imbeddings of symmetric domains into a Siegel space, Amer. J. Math., Volume 87 (1965), pp. 425-461

[15] Toledo, D. Representations of surface groups in complex hyperbolic space, J. Differential Geom., Volume 29 (1989), pp. 125-133

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