Dominating surface-group representations into PSL₂ (ℂ) in the relative representation variety

2020/03/30 by Gupta, Subhojoy, Su, Weixu · 1 citation
#FOS: Mathematics #Geometric Topology (math.GT) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2003.13572

Abstract

Let ρ be a representation of the fundamental group of a punctured surface into PSL₂ (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 PSL₂ (ℂ)-representations. Our proof involves straightening the pleated plane in ℍ³ determined by the Fock-Goncharov coordinates of a framed representation, and applying strip-deformations.

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• Harmonic maps and framed PSL₂(ℂ)-representations

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