31 citations · 113 across the 46 of their papers we have counts for
35 papers · 1 filter
Optimizing the Upper-Bound Constant for the Crossing Number of Polynomial Curve Systems
Hyungryul Baik
Baader, Jörg, and Parlier recently established an upper bound for the crossing number of curve systems of size on a genus surface, obtaining a leading coeffic…
Uniform Perfectness and Centers in Sublinearly Morse Boundaries
Hyungryul Baik
The --Morse boundary was introduced for CAT(0) spaces by Qing and Rafi and extended to proper geodesic spaces by Qing, Rafi, and Tiozzo. Motivated by Han and Liu's work on unifo…
Normal generators for mapping class groups
Hyungryul Baik, Dongryul M. Kim
In this chapter, we discuss normal generators for mapping class groups of surfaces. Especially, we focus on the relation between normal generation of a mapping class with its asymp…
Reconstruction of Anosov flows from infinity
Hyungryul Baik, Chenxi Wu, Bojun Zhao
Every pseudo-Anosov flow in a closed -manifold gives rise to an action of on a circle from infinity \cite{Fen12}, with a pair of invariant \…
On Translation Lengths of Pseudo-Anosov Maps on the Curve Graph
Hyungryul Baik, Changsub Kim
We show that a pseudo-Anosov map constructed as a product of the large power of Dehn twists of two filling curves always has a geodesic axis on the curve graph of the surface. We a…
Groups acting on veering pairs and Kleinian groups
Hyungryul Baik, Hongtaek Jung, KyeongRo Kim
We show that some laminar group which has an invariant veering pair of laminations is a hyperbolic 3-orbifold group. On the way, we show that from a veering pair of laminations, on…
Topological entropy of pseudo-Anosov maps on punctured surfaces vs. homology of mapping tori
Hyungryul Baik, Juhun Baik, Changsub Kim +1
We investigate the relation between the topological entropy of pseudo-Anosov maps on surfaces with punctures and the rank of the first homology of their mapping tori. On the surfac…
Reducible normal generators for mapping class groups are abundant
Hyungryul Baik, Dongryul M. Kim, Chenxi Wu
In this article, we study the normal generation of the mapping class group. We first show that a mapping class is a normal generator if its restriction on the invariant subsurface…
Random walks on mapping class groups
Inhyeok Choi, Hyungryul Baik
This survey is concerned with random walks on mapping class groups. We illustrate how the actions of mapping class groups on Teichmüller spaces or curve complexes reveal the nature…
Characterization of Fuchsian groups as laminar groups & the structure theorem of hyperbolic 2-orbifolds
Hyungryul Baik, KyeongRo Kim
Thurston and Calegari-Dunfield showed that the fundamental group of some tautly foliated hyperbolic 3-manifold acts on the circle in a distinctive way that the action preserves som…
Foliations from left orders
Hyungryul Baik, Sebastian Hensel, Chenxi Wu
We describe a construction which takes as an input a left order of the fundamental group of a manifold, and outputs a (singular) foliation of this manifold which is analogous to a…
Minimal asymptotic translation lengths on curve complexes and homology of mapping tori
Hyungryul Baik, Dongryul M. Kim, Chenxi Wu
Let be a closed orientable surface of genus . Consider the minimal asymptotic translation length on the Teichmüller space of , among pseud…
Linear growth of translation lengths of random isometries on Gromov hyperbolic spaces and Teichmüller spaces
Hyungryul Baik, Inhyeok Choi, Dongryul M. Kim
We investigate the translation lengths of group elements that arise in random walks on the isometry groups of Gromov hyperbolic spaces. In particular, without any moment condition,…
Simple length spectra as moduli for hyperbolic surfaces and rigidity of length identities
Hyungryul Baik, Inhyeok Choi, Dongryul M. Kim
In this article, we revisit classical length identities enjoyed by simple closed curves on hyperbolic surfaces. We state and prove the rigidity of such identities over Teichmüller…
On the asymptotic translation lengths on the sphere complexes and the generalized fibered cone
Hyungryul Baik, Dongryul M. Kim, Chenxi Wu
In this paper, we study the asymptotic translation lengths on the sphere complexes of monodromies of a manifold fibered over the circle. Given a compact mapping torus, we define a…
Topological and dynamical properties of Torelli groups of partitioned surfaces
Hyungryul Baik, Hyunshik Shin, Philippe Tranchida
Putman introduced a notion of a partitioned surface which is a surface with boundary with decoration restricting how the surface can be embedded into larger surfaces, and defined t…
On the surjectivity of the Symplectic representation of the mapping class group
Hyungryul Baik, Inhyeok Choi, Dongryul M. Kim
In this note, we study the symplectic representation of the mapping class group. In particular, we discuss the surjecivity of the representation restricted to certain mapping class…
Topological entropy of pseudo-Anosov maps from a typical Thurston's construction
Hyungryul Baik, Inhyeok Choi, Dongryul M. Kim
In this paper, we develop a way to extract information about a random walk associated with a typical Thurston's construction. We first observe that a typical Thurston's constructio…
Laminar groups and 3-manifolds
Hyungryul Baik, KyeongRo Kim
Thurston showed that the fundamental group of a close atoroidal 3-manifold admitting a co-oriented taut foliation acts faithfully on the circle by orientation-preserving homeomorph…
Asymptotic translation lengths and normal generation for pseudo-Anosov monodromies of fibered 3-manifolds
Hyungryul Baik, Eiko Kin, Hyunshik Shin +1
Let be a hyperbolic fibered 3-manifold. We study properties of sequences of fibers and monodromies for primitive integral classes in the fibered cone of $M…
On Translation Lengths of Anosov Maps on Curve Graph of Torus
Hyungryul Baik, Changsub Kim, Sanghoon Kwak +1
We show that an Anosov map has a geodesic axis on the curve graph of a torus. The direct corollary of our result is the stable translation length of an Anosov map on the curve grap…
Minimal asymptotic translation lengths of Torelli groups and pure braid groups on the curve graph
Hyungryul Baik, Hyunshik Shin
In this paper, we show that the minimal asymptotic translation length of the Torelli group of the surface of genus on the curve graph asymptotically behav…
An upper bound on the asymptotic translation lengths on the curve graph and fibered faces
Hyungryul Baik, Hyunshik Shin, Chenxi Wu
We study the asymptotic behavior of the asymptotic translation lengths on the curve complexes of pseudo-Anosov monodromies in a fibered cone of a fibered hyperbolic 3-manifold …
An algorithm to compute the Teichmueller polynomial from matrices
Hyungryul Baik, Chenxi Wu
In their precedent work, the authors constructed closed oriented hyperbolic surfaces with pseudo-Anosov homeomorphisms from certain class of integral matrices. In this paper, we pr…