Dominating surface-group representations into $\mathrm{PSL}_2 (\mathbb{C})$ in the relative representation variety
Year: 2020
Type: preprint
Abstract: Let $ρ$ 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 representation that strictly dominates $ρ$ in the simple length spectrum, and preserves the boundary lengths. This extends a result of Gueritaud-Kassel-Wolff to the case of $\mathrm{PSL}_2 (\mathbb{C})$-representations. Our proof involves straightening the pleated plane in $\mathbb{H}^3$ determined by the Fock-Goncharov coordinates of a framed representation, and applying strip-deformations.
Source: arXiv (Cornell University)
Authors: Gupta, Subhojoy, Su, Weixu
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W3014062700