Geodesic
Thurston’s asymmetric metrics for Anosov representations
León Carvajales1 orcid ; Xian Dai2 orcid ; Beatrice Pozzetti3 orcid ; Anna Wienhard4 orcid
1Universidad de la República, Montevideo, Uruguay
2Ruhr-Universität Bochum, Germany
3Ruprecht-Karls Universität Heidelberg, Germany
4Max Planck Institute for Mathematics in the Sciences, Leipzig, Germany
Groups, geometry, and dynamics, Tome 19 (2025) no. 3, pp. 731-796

Voir la notice de l'article provenant de la source EMS Press

DOI

We provide a good dynamical framework allowing to generalize Thurston’s asymmetric metric and the associated Finsler norm from Teichmüller space to large classes of Anosov representations. In many cases, including the space of Hitchin representations, this gives a (possibly asymmetric) Finsler distance. In some cases, we explicitly compute the associated Finsler norm.
DOI : 10.4171/ggd/810
Classification : 53C15
Mots-clés : Thurston’s asymmetric metrics, Anosov representations, thermodynamic formalism

León Carvajales  1   ; Xian Dai  2   ; Beatrice Pozzetti  3   ; Anna Wienhard  4

1 Universidad de la República, Montevideo, Uruguay
2 Ruhr-Universität Bochum, Germany
3 Ruprecht-Karls Universität Heidelberg, Germany
4 Max Planck Institute for Mathematics in the Sciences, Leipzig, Germany 
León Carvajales; Xian Dai; Beatrice Pozzetti; Anna Wienhard. Thurston’s asymmetric metrics for Anosov representations. Groups, geometry, and dynamics, Tome 19 (2025) no. 3, pp. 731-796. doi: 10.4171/ggd/810
@article{10_4171_ggd_810,
     author = {Le\'on Carvajales and Xian Dai and Beatrice Pozzetti and Anna Wienhard},
     title = {Thurston{\textquoteright}s asymmetric metrics for {Anosov} representations},
     journal = {Groups, geometry, and dynamics},
     pages = {731--796},
     year = {2025},
     volume = {19},
     number = {3},
     doi = {10.4171/ggd/810},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/ggd/810/}
}
TY  - JOUR
AU  - León Carvajales
AU  - Xian Dai
AU  - Beatrice Pozzetti
AU  - Anna Wienhard
TI  - Thurston’s asymmetric metrics for Anosov representations
JO  - Groups, geometry, and dynamics
PY  - 2025
SP  - 731
EP  - 796
VL  - 19
IS  - 3
UR  - http://geodesic.mathdoc.fr/articles/10.4171/ggd/810/
DO  - 10.4171/ggd/810
ID  - 10_4171_ggd_810
ER  - 
%0 Journal Article
%A León Carvajales
%A Xian Dai
%A Beatrice Pozzetti
%A Anna Wienhard
%T Thurston’s asymmetric metrics for Anosov representations
%J Groups, geometry, and dynamics
%D 2025
%P 731-796
%V 19
%N 3
%U http://geodesic.mathdoc.fr/articles/10.4171/ggd/810/
%R 10.4171/ggd/810
%F 10_4171_ggd_810

Cité par Sources :