Comptes Rendus
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, Volume 336 (2003) no. 5, pp. 387-390.

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

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

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/S1631-073X(03)00065-7

Marc Burger 1 ; Alessandra Iozzi 2 ; Anna Wienhard 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
@article{CRMATH_2003__336_5_387_0,
     author = {Marc Burger and Alessandra Iozzi and Anna Wienhard},
     title = {Surface group representations with maximal {Toledo} invariant},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {387--390},
     publisher = {Elsevier},
     volume = {336},
     number = {5},
     year = {2003},
     doi = {10.1016/S1631-073X(03)00065-7},
     language = {en},
}
TY  - JOUR
AU  - Marc Burger
AU  - Alessandra Iozzi
AU  - Anna Wienhard
TI  - Surface group representations with maximal Toledo invariant
JO  - Comptes Rendus. Mathématique
PY  - 2003
SP  - 387
EP  - 390
VL  - 336
IS  - 5
PB  - Elsevier
DO  - 10.1016/S1631-073X(03)00065-7
LA  - en
ID  - CRMATH_2003__336_5_387_0
ER  - 
%0 Journal Article
%A Marc Burger
%A Alessandra Iozzi
%A Anna Wienhard
%T Surface group representations with maximal Toledo invariant
%J Comptes Rendus. Mathématique
%D 2003
%P 387-390
%V 336
%N 5
%I Elsevier
%R 10.1016/S1631-073X(03)00065-7
%G en
%F CRMATH_2003__336_5_387_0
Marc Burger; Alessandra Iozzi; Anna Wienhard. Surface group representations with maximal Toledo invariant. Comptes Rendus. Mathématique, Volume 336 (2003) no. 5, pp. 387-390. doi : 10.1016/S1631-073X(03)00065-7. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/S1631-073X(03)00065-7/

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

[6] J.L. Clerc; B. Ørsted 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] A. Domic; D. Toledo 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] L. Hernàndez Lamoneda Maximal representations of surface groups in bounded symmetric domains, Trans. Amer. Math. Soc., Volume 324 (1991), pp. 405-420

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

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

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

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

  • J. Maxwell Riestenberg A quantified local-to-global principle for Morse quasigeodesics, Groups, Geometry, and Dynamics, Volume 19 (2025) no. 1, pp. 37-107 | DOI:10.4171/ggd/829 | Zbl:7990868
  • Steven Bradlow; Brian Collier; Oscar García-Prada; Peter B. Gothen; André Oliveira A general Cayley correspondence and higher rank Teichmüller spaces, Annals of Mathematics. Second Series, Volume 200 (2024) no. 3, pp. 803-892 | DOI:10.4007/annals.2024.200.3.1 | Zbl:7995682
  • Olivier Biquard; Brian Collier; Oscar García-Prada; Domingo Toledo Arakelov-Milnor inequalities and maximal variations of Hodge structure, Compositio Mathematica, Volume 159 (2023) no. 5, pp. 1005-1041 | DOI:10.1112/s0010437x23007157 | Zbl:1522.14047
  • Óscar García Prada Higgs bundles and higher Teichmüller spaces, Handbook of Teichmüller theory. Volume VII, Berlin: European Mathematical Society (EMS), 2020, pp. 239-285 | DOI:10.4171/203-1/9 | Zbl:1446.30072
  • Jérémy Toulisse Higgs bundles, pseudo-hyperbolic geometry and maximal representations, Séminaire de théorie spectrale et géométrie, Volume 34 (2017), p. 97 | DOI:10.5802/tsg.357
  • Tengren Zhang Degeneration of Hitchin representations along internal sequences, Geometric and Functional Analysis. GAFA, Volume 25 (2015) no. 5, pp. 1588-1645 | DOI:10.1007/s00039-015-0342-7 | Zbl:1327.30054
  • Peter B. Gothen Representations of surface groups and Higgs bundles, Moduli Spaces (2014), p. 151 | DOI:10.1017/cbo9781107279544.004
  • Michelle Bucher; Marc Burger; Alessandra Iozzi A dual interpretation of the Gromov-Thurston proof of Mostow rigidity and volume rigidity for representations of hyperbolic lattices, Trends in harmonic analysis. Selected papers of the conference on harmonic analysis, Rome, Italy, May 30–June 4, 2011, Berlin: Springer, 2013, pp. 47-76 | DOI:10.1007/978-88-470-2853-1_4 | Zbl:1268.53056
  • Marc Burger; Alessandra Iozzi Bounded cohomology and totally real subspaces in complex hyperbolic geometry, Ergodic Theory and Dynamical Systems, Volume 32 (2012) no. 2, pp. 467-478 | DOI:10.1017/s0143385711000393 | Zbl:1318.32026
  • Adam S. Sikora Character varieties, Transactions of the American Mathematical Society, Volume 364 (2012) no. 10, pp. 5173-5208 | DOI:10.1090/s0002-9947-2012-05448-1 | Zbl:1291.14022
  • Danny Calegari; Joel Louwsma Immersed surfaces in the modular orbifold., Proceedings of the American Mathematical Society, Volume 139 (2011) no. 7, pp. 2295-2308 | DOI:10.1090/s0002-9939-2011-10911-0 | Zbl:1276.20049
  • Marc Burger; Alessandra Iozzi; Anna Wienhard Surface group representations with maximal Toledo invariant, Annals of Mathematics. Second Series, Volume 172 (2010) no. 1, pp. 517-566 | DOI:10.4007/annals.2010.172.517 | Zbl:1208.32014
  • Pierre-Emmanuel Caprace; Koji Fujiwara Rank-one isometries of buildings and quasi-morphisms of Kac-Moody groups., Geometric and Functional Analysis. GAFA, Volume 19 (2010) no. 5, pp. 1296-1319 | DOI:10.1007/s00039-009-0042-2 | Zbl:1206.20046
  • Gabi Ben Simon; Dietmar A. Salamon Homogeneous quasimorphisms on the symplectic linear group., Israel Journal of Mathematics, Volume 175 (2010), pp. 221-224 | DOI:10.1007/s11856-010-0010-4 | Zbl:1205.20051
  • Nicolas Monod On the bounded cohomology of semi-simple groups, S-arithmetic groups and products, Journal für die reine und angewandte Mathematik (Crelles Journal), Volume 2010 (2010) no. 640 | DOI:10.1515/crelle.2010.024
  • Marc Burger; Alessandra Iozzi; Anna Wienhard Tight homomorphisms and Hermitian symmetric spaces, Geometric and Functional Analysis. GAFA, Volume 19 (2009) no. 3, pp. 678-721 | DOI:10.1007/s00039-009-0020-8 | Zbl:1188.53050
  • Danny Calegari Faces of the scl norm ball., Geometry Topology, Volume 13 (2009) no. 3, pp. 1313-1336 | DOI:10.2140/gt.2009.13.1313 | Zbl:1228.20032
  • Inkang Kim; Pierre Pansu Local rigidity in quaternionic hyperbolic space, Journal of the European Mathematical Society (JEMS), Volume 11 (2009) no. 6, pp. 1141-1164 | DOI:10.4171/jems/177 | Zbl:1203.53046
  • Vincent Koziarz; Julien Maubon Representations of complex hyperbolic lattices into rank 2 classical Lie groups of Hermitian type, Geometriae Dedicata, Volume 137 (2008), pp. 85-111 | DOI:10.1007/s10711-008-9288-3 | Zbl:1159.22006
  • Mike Krebs Toledo invariants of 2-orbifolds and Higgs bundles on elliptic surfaces, Michigan Mathematical Journal, Volume 56 (2008) no. 1, pp. 3-27 | DOI:10.1307/mmj/1213972395 | Zbl:1163.14009
  • Stephen Wang Representations of surface groups and right-angled Artin groups in higher rank, Algebraic Geometric Topology, Volume 7 (2007), pp. 1099-1117 | DOI:10.2140/agt.2007.7.1099 | Zbl:1133.20024
  • Steven B. Bradlow; Oscar García-Prada; Peter B. Gothen Maximal surface group representations in isometry groups of classical Hermitian symmetric spaces, Geometriae Dedicata, Volume 122 (2006), pp. 185-213 | DOI:10.1007/s10711-007-9127-y | Zbl:1132.14029
  • Marc Burger; Alessandra Iozzi Bounded differential forms, generalized Milnor-Wood inequality and an application to deformation rigidity, Geometriae Dedicata, Volume 125 (2007), pp. 1-23 | DOI:10.1007/s10711-006-9108-6 | Zbl:1134.53020
  • François Labourie Cross ratios, surface groups, PSL(n,R) and diffeomorphisms of the circle, Publications Mathématiques, Volume 106 (2007), pp. 139-213 | DOI:10.1007/s10240-007-0009-5 | Zbl:1203.30044
  • Anna Wienhard The action of the mapping class group on maximal representations., Geometriae Dedicata, Volume 120 (2006), pp. 179-191 | DOI:10.1007/s10711-006-9079-7 | Zbl:1175.32007
  • François Labourie Anosov flows, surface groups and curves in projective space, Inventiones Mathematicae, Volume 165 (2006) no. 1, pp. 51-114 | DOI:10.1007/s00222-005-0487-3 | Zbl:1103.32007
  • Marc Burger; Alessandra Iozzi Bounded Kähler class rigidity of actions on Hermitian symmetric spaces, Annales Scientifiques de l'École Normale Supérieure. Quatrième Série, Volume 37 (2004) no. 1, pp. 77-103 | DOI:10.1016/j.ansens.2003.09.001 | Zbl:1061.32016
  • Anna Katharina Wienhard Bounded cohomology and geometry, Bonner Mathematische Schriften, 368, Bonn: Univ. Bonn, Mathematisches Institut (Dissertation), 2004 | Zbl:1084.32013
  • Anna Wienhard A generalisation of Teichmüller space in the Hermitian context, Séminaire de théorie spectrale et géométrie. Année 2003–2004, St. Martin d'Hères: Université de Grenoble I, Institut Fourier, 2004, pp. 103-123 | Zbl:1070.32012

Cité par 29 documents. Sources : Crossref, zbMATH

Commentaires - Politique