|Dept.||IBS 기하학 수리물리 연구단|
The fundamental groups of many 3-manifolds can act on the circle. Examples include closed orientable 3-manifolds with a taut foliations, closed orientable 3-manifolds with a pseudo-Anosov flow, hyperbolic 3-manifolds with a quasi-geodesic flows and so on. A fascinating feature is that all of these actions leave some circle laminations invariant. In this talk, I will present the inverse problem, asking whether a given group is the fundamental group of a 3-manifold if it acts on the circle preserving circle laminations. The answer to this problem very depends on properties of the invariant laminations. I will introduce veering pair of circle laminations, which is motivated by recent work of Schleimer and Segerman on veering triangulations, and show that a group acting on the circle with an invariant veering pair must be the fundamental group of an irreducible 3-orbifold. This is joint work with Hyungryul Baik and KyeongRo Kim.