Holonomy map fibers of $\mathbb{C}{\mathrm{P}}^1$-structures in moduli space

Abstract

Let $S$ be a closed oriented surface of genus $g\ge 2$. Fix an arbitrary non-elementary representation $\rho :{\pi }_1(S)\to {\mathrm{SL}}_2(\mathbb{C})$ and consider all marked (complex) projective structures on $S$ with holonomy $\rho$. We show that their underlying conformal structures are dense in the moduli space of $S$.

26 pages, 6 figures. To appear in Journal of Topology

References in corpus (3)

• 2 π-grafting and complex projective structures, I
• Asymptoticity of grafting and Teichmüller rays I
• 2π-grafting and complex projective structures with generic holonomy

Cited by in corpus (2)

• Translation surfaces and periods of meromorphic differentials
• Local deformations of branched projective structures: Schiffer variations and the Teichmüller map