Geodesic
Compatible pants decomposition for $\mathrm{SL}_{2}(\mathbb{C})$ representations of surface groups
Renaud Detcherry1 orcid ; Thomas Le Fils2 ; Ramanujan Santharoubane3
1Université Bourgogne Franche-Comté, Dijon, France
2Sorbonne Université, Paris, France
3Université Paris-Saclay, Orsay Cedex, France
Groups, geometry, and dynamics, Tome 19 (2025) no. 3, pp. 861-877

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

DOI

For any irreducible representation of a surface group into SL2​(C), we show that there exists a pants decomposition where the restriction to any pair of pants is irreducible and where no curve of the decomposition is sent to a trace ±2 element. We prove a similar property for SO3​-representations. We also investigate the type of pants decomposition that can occur in this setting for a given representation. This result was announced by Detcherry and Santharoubane (2022), motivated by the study of the Azumaya locus of the skein algebra of surfaces at roots of unity.
DOI : 10.4171/ggd/797
Classification : 57K20, 57K31
Mots-clés : mapping class group, surface group representations

Renaud Detcherry  1   ; Thomas Le Fils  2   ; Ramanujan Santharoubane  3

1 Université Bourgogne Franche-Comté, Dijon, France
2 Sorbonne Université, Paris, France
3 Université Paris-Saclay, Orsay Cedex, France 
Renaud Detcherry; Thomas Le Fils; Ramanujan Santharoubane. Compatible pants decomposition for $\mathrm{SL}_{2}(\mathbb{C})$ representations of surface groups. Groups, geometry, and dynamics, Tome 19 (2025) no. 3, pp. 861-877. doi: 10.4171/ggd/797
@article{10_4171_ggd_797,
     author = {Renaud Detcherry and Thomas Le Fils and Ramanujan Santharoubane},
     title = {Compatible pants decomposition for $\mathrm{SL}_{2}(\mathbb{C})$ representations of surface groups},
     journal = {Groups, geometry, and dynamics},
     pages = {861--877},
     year = {2025},
     volume = {19},
     number = {3},
     doi = {10.4171/ggd/797},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/ggd/797/}
}
TY  - JOUR
AU  - Renaud Detcherry
AU  - Thomas Le Fils
AU  - Ramanujan Santharoubane
TI  - Compatible pants decomposition for $\mathrm{SL}_{2}(\mathbb{C})$ representations of surface groups
JO  - Groups, geometry, and dynamics
PY  - 2025
SP  - 861
EP  - 877
VL  - 19
IS  - 3
UR  - http://geodesic.mathdoc.fr/articles/10.4171/ggd/797/
DO  - 10.4171/ggd/797
ID  - 10_4171_ggd_797
ER  - 
%0 Journal Article
%A Renaud Detcherry
%A Thomas Le Fils
%A Ramanujan Santharoubane
%T Compatible pants decomposition for $\mathrm{SL}_{2}(\mathbb{C})$ representations of surface groups
%J Groups, geometry, and dynamics
%D 2025
%P 861-877
%V 19
%N 3
%U http://geodesic.mathdoc.fr/articles/10.4171/ggd/797/
%R 10.4171/ggd/797
%F 10_4171_ggd_797

Cité par Sources :