Subgroups of genus-2 quasi-Fuchsian groups and cocompact Kleinian groups

Rao, Zhenghao¹

¹ Department of Mathematics, Rutgers University, Piscataway, NJ, United States, Department of Mathematics, Brown University, Providence, RI, United States

Geometry & topology, Tome 29 (2025) no. 1, pp. 495-548.

Résumé

We wish 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 $\nu >0$ we will find a surface subgroup $H$ of $G$ that is $(1+\nu )$-quasiconformally conjugate to a finite-index subgroup $F<\Gamma$.

Détail

Keywords: quasi-Fuchsian groups, hyperbolic $3$-manifolds, surface subgroups

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