Compatible pants decompositions for $\mathrm{SL}_2(\mathbb{C})$-representations of surface groups
Geometric Topology
2022-10-19 v1
Abstract
For any irreducible representation of a surface group into , 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 element. We prove a similar property for -representations. We also investigate the type of pants decomposition that can occur in this setting for a given representation. This result was announced in a previous paper of the first and third named authors, motivated by the study of the Azumaya locus of the skein algebra of surfaces at roots of unity.
Cite
@article{arxiv.2210.09854,
title = {Compatible pants decompositions for $\mathrm{SL}_2(\mathbb{C})$-representations of surface groups},
author = {Renaud Detcherry and Thomas Le Fils and Ramanujan Santharoubane},
journal= {arXiv preprint arXiv:2210.09854},
year = {2022}
}