|Date||Sep 07, 2021|
When we study 3-manifolds, we can think of 3-manifolds as unions of disjoint collections of 2-manifolds. Such structures are called foliations. Each 2-manifold in foliations is called a leaf. The configuration of leaves gives a 1-dimensional manifold which contains the transversal information. By Thurston and Calegari-Dunfield, it was shown that any fundamental group of an atoroidal 3-manifold with taut foliation acts on a circle, so-called a universal circle, by orientation preserving homeomorphisms. From the proof, we may observe that the universal circle actions preserve pairs of laminations of the circle. In this talk, I introduce the study of laminar groups which is a subgroup of orientation preserving circle homeomorphisms, preserving circle laminations.