Hyungryul Baik

Right-angled Artin groups in the C ∞ diffeomorphism group of the real line

We prove that every right-angled Artin group embeds into the C∞ diffeomorphism group of the real line. As a corollary, we show every limit group, and more generally every countable residually RAAG group, embeds into the C∞ diffeomorphism group of the real line.

Constructing pseudo-Anosov maps with given dilatations

In this paper, we give sufficient conditions for a Perron number, given as the leading eigenvalue of an aperiodic matrix, to be a pseudo-Anosov dilatation of a compact surface. We give an explicit construction of the surface and the map when the sufficient condition is met.

Fuchsian groups, circularly ordered groups and dense invariant laminations on the circle

We propose a program to study groups acting faithfully on S 1 in terms of numbers of pairwise transverse dense invariant laminations. We give some examples of groups that admit a small number of invariant laminations as an introduction to such groups. The main focus of the present paper is to characterize Fuchsian groups in this scheme. We prove a group acting on S 1 is conjugate to a Fuchsian group if and only if it admits three very full laminations with a variation on the transversality condition. Some partial results toward a similar characterization of hyperbolic 3‐manifold groups that fiber over the circle have been obtained. This work was motivated by the universal circle theory for tautly foliated 3‐manifolds developed by Thurston, Calegari and Dunfield.