Dominating surface-group representations into ${\mathrm{PSL}}_2(\mathbb{C})$ in the relative representation variety

Subhojoy Gupta, Weixu Su

Let $\rho$ be a representation of the fundamental group of a punctured surface into ${\mathrm{PSL}}_2(\mathbb{C})$ that is not Fuchsian. We prove that there exists a Fuchsian represent…