Domains of discontinuity for surface groups

Guichard, Olivier; Wienhard, Anna

doi:10.1016/j.crma.2009.06.013

Geometry/Topology

Domains of discontinuity for surface groups
[Quotients compacts et groupes de surfaces]

Présenté par : Jean-Michel Bismut

Guichard, Olivier ^1,² ; Wienhard, Anna ³

¹ CNRS, laboratoire de mathématiques d'Orsay, 91405 Orsay cedex, France
² Université Paris-Sud, 91405 Orsay cedex, France
³ Department of Mathematics, Princeton University, Fine Hall, Washington Road, Princeton, NJ 08544-1000, USA

Comptes Rendus. Mathématique, Tome 347 (2009) no. 17-18, pp. 1057-1060.

Résumé
Abstract

Soit $π_{1} (Σ)$ le groupe fondamental d'une surface de Riemann connexe, fermée et de genre supérieur et soit G un groupe de Lie semi-simple. Pour toute représentation Anosov $ρ : π_{1} (Σ) \to G$ , nous construisons un ouvert de la variété drapeau $G / Q$ sur lequel $π_{1} (Σ)$ agit proprement avec quotient compact.

Let Σ be a closed connected orientable surface of negative Euler characteristic and G a semisimple Lie group. For any Anosov representation $ρ : π_{1} (Σ) \to G$ we construct domains of discontinuity with compact quotient for the action of $π_{1} (Σ)$ on flag varieties $G / Q$ .

Reçu le : 2009-06-14
Accepté le : 2009-06-18
Publié le : 2009-07-11

DOI : 10.1016/j.crma.2009.06.013

Affiliations des auteurs :

Guichard, Olivier ^{1, 2} ; Wienhard, Anna ³

@article{CRMATH_2009__347_17-18_1057_0,
     author = {Guichard, Olivier and Wienhard, Anna},
     title = {Domains of discontinuity for surface groups},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {1057--1060},
     publisher = {Elsevier},
     volume = {347},
     number = {17-18},
     year = {2009},
     doi = {10.1016/j.crma.2009.06.013},
     language = {en},
     url = {http://www.numdam.org/articles/10.1016/j.crma.2009.06.013/}
}

TY  - JOUR
AU  - Guichard, Olivier
AU  - Wienhard, Anna
TI  - Domains of discontinuity for surface groups
JO  - Comptes Rendus. Mathématique
PY  - 2009
SP  - 1057
EP  - 1060
VL  - 347
IS  - 17-18
PB  - Elsevier
UR  - http://www.numdam.org/articles/10.1016/j.crma.2009.06.013/
DO  - 10.1016/j.crma.2009.06.013
LA  - en
ID  - CRMATH_2009__347_17-18_1057_0
ER  -

%0 Journal Article
%A Guichard, Olivier
%A Wienhard, Anna
%T Domains of discontinuity for surface groups
%J Comptes Rendus. Mathématique
%D 2009
%P 1057-1060
%V 347
%N 17-18
%I Elsevier
%U http://www.numdam.org/articles/10.1016/j.crma.2009.06.013/
%R 10.1016/j.crma.2009.06.013
%G en
%F CRMATH_2009__347_17-18_1057_0

Guichard, Olivier; Wienhard, Anna. Domains of discontinuity for surface groups. Comptes Rendus. Mathématique, Tome 347 (2009) no. 17-18, pp. 1057-1060. doi : 10.1016/j.crma.2009.06.013. http://www.numdam.org/articles/10.1016/j.crma.2009.06.013/

Bibliographie
Cité par

[1] Barbot, T. Three-dimensional Anosov flag manifolds, 2005 | arXiv

[2] Barbot, T. Quasi-Fuchsian AdS representations are Anosov, 2007 | arXiv

[3] M. Burger, A. Iozzi, A. Wienhard, Maximal representations and Anosov structures, in preparation

[4] Burger, M.; Iozzi, A.; Labourie, F.; Wienhard, A. Maximal representations of surface groups: Symplectic Anosov structures, Pure and Applied Mathematics Quarterly. Special Issue: In Memory of Armand Borel, Volume 1 (2005) no. 2, pp. 555-601

[5] Fock, V.; Goncharov, A. Moduli spaces of local systems and higher Teichmüller theory, Publ. Math. Inst. Hautes Études Sci., Volume 103 (2006), pp. 1-211

[6] Fulton, W.; Harris, J. Representation Theory, Graduate Texts in Mathematics, vol. 129, Springer-Verlag, New York, 1991

[7] Guichard, O. Composantes de Hitchin et représentations hyperconvexes de groupes de surface, J. Differential Geom., Volume 80 (2008) no. 3, pp. 391-431

[8] Guichard, O.; Wienhard, A. Topological invariants of Anosov representations, 2009 | arXiv

[9] Hitchin, N. Lie groups and Teichmüller space, Topology, Volume 31 (1992) no. 3, pp. 449-473

[10] Labourie, F. Anosov flows, surface groups and curves in projective space, Invent. Math., Volume 165 (2006) no. 1, pp. 51-114

[11] Mérigot, Q. Anosov AdS representations are quasi-Fuchsian, 2007 | arXiv

Cité par Sources :