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Surface Subgroups of Cocompact Kleinian Groups

  • Zhenghao Rao (Brown University)
E2 10 (Leon-Lichtenstein)

Abstract

Kahn and Markovic proved the Surface Subgroup conjecture for closed hyperbolic 3-manifolds more than ten years ago. The surface subgroup they constructed can be as close as possible to Fuchsian. However, a closed hyperbolic 3-manifold can also have surface subgroups far away from being Fuchsian. Our result states that provided any genus-2 quasi-Fuchsian group Γ and cocompact Kleinian group G, then for any K>1, one can find a surface subgroup H of G that is K-quasiconformally conjugate to a finite index subgroup F<Γ. We will point out the difference between the above theorem and the original Surface Subgroup Theorem, discuss the proof idea, and introduce some applications.

Katharina Matschke

MPI for Mathematics in the Sciences Contact via Mail

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