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

Rao, Zhenghao¹

¹Department of Mathematics, Brown University, Providence, RI, United States, Department of Mathematics, Rutgers University, Piscataway, NJ, 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 Γ and cocompact Kleinian group G, then for any ν > 0 we will find a surface subgroup H of G that is (1+ν)-quasiconformally conjugate to a finite-index subgroup F < Γ.

Détail

DOI : 10.2140/gt.2025.29.495

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

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