Appears in collection : 2024 - T2 - WS1 - Low dimensional actions

Thurston showed the universal circle theorem as a first step of the proof of the geometrization conjecture of tautly foliated three manifolds. The theorem says that the fundamental group of a closed three manifold slithering over the circle acts on the circle preserving a pair of laminations. In this talk, I talk about the converse of the universal circle theorem in terms of laminar groups. Also, I will overview recent results about the laminar groups and discuss related open problems. This talk is based on works with Harry Hyungryul Baik and Hongtaek Jung.