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

Shinpei Baba; Subhojoy Gupta

doi:10.1112/jtopol/jtv013

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

Geometric Topology 2015-06-12 v2 Differential Geometry

Authors: 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 $S$ .

Keywords

holomorphic mappings moduli spaces algebraic topology

Cite

@article{arxiv.1402.5445,
  title  = {Holonomy map fibers of $\mathbb{C}{\rm P}^1$-structures in moduli space},
  author = {Shinpei Baba and Subhojoy Gupta},
  journal= {arXiv preprint arXiv:1402.5445},
  year   = {2015}
}

Comments

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

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

Abstract

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