Subgroups of Genus-2 Quasi-Fuchsian groups and Cocompact Kleinian Groups

Zhenghao Rao

doi:10.2140/gt.2025.29.495

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arXiv · 2302.01995

Subgroups of Genus-2 Quasi-Fuchsian groups and Cocompact Kleinian Groups

Zhenghao Rao

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Abstract

In this paper, we want to control the geometry of some surface subgroups of a cocompact Kleinian group. More precisely, provided any genus-2 quasi-Fuchsian group $\Gamma$ and cocompact Kleinian group $G$, then for any $K>1$, we will find a surface subgroup $H$ of $G$ that is $K$-quasiconformally conjugate to a finite index subgroup $F<\Gamma$.

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Zhenghao Rao. 2023-02-03. Subgroups of Genus-2 Quasi-Fuchsian groups and Cocompact Kleinian Groups. https://doi.org/10.2140/gt.2025.29.495

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