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

Shinpei Baba; Subhojoy Gupta

doi:10.1112/jtopol/jtv013

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arXiv · 1402.5445

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

Shinpei Baba·Subhojoy Gupta

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Abstract

Let $S$ be a closed oriented surface of genus $g\geq 2$. Fix an arbitrary non-elementary representation $\rho\colon\pi_1(S)\to {\rm SL}_2(\mathbb{C})$ 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 $S$.

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Shinpei Baba, Subhojoy Gupta. 2014-02-21. Holonomy map fibers of $\mathbb{C}{\rm P}^1$-structures in moduli space. https://doi.org/10.1112/jtopol%2Fjtv013

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