Compatible pants decompositions for ${\mathrm{SL}}_2(\mathbb{C})$-representations of surface groups

Renaud Detcherry, Thomas Le Fils, Ramanujan Santharoubane

For any irreducible representation of a surface group into ${\mathrm{SL}}_2(\mathbb{C})$, we show that there exists a pants decomposition where the restriction to any pair of pants i…