Sang-hyun Kim

activity

20062026

most citedEmbedability between right-angled Artin groups

103 citations · 240 across the 31 of their papers we have counts for

collaborators

34 papers

math.GR2026

A note on the proof of nonamenability of F

Sang-hyun Kim, Yash Lodha

The goal of this note is to provide a human written exposition of OpenAI's recent proof that Thompson's group F is nonamenable.

math.GR2026

Hyperbolicity and obstructions to PL actions of the circle

Leonardo Dinamarca, Maximiliano Escayola, Sang-hyun Kim +1

We prove the following ``Torus Trichotomy Theorem'': every finitely generated subgroup of $\pls$ is either virtually free, a central extension of a cocompact Fuchsian group by a fi…

math.GR2026

Small growth rates of free groups

Koji Fujiwara, Sang-hyun Kim, Ryokichi Tanaka

We introduce the notion of a Magnus marking for a finite generating set of a group and prove a certain expansion property. Using this property, we determine the second and third sm…

math.GR2025

Elementary equivalence and diffeomorphism groups of smooth manifolds

Sang-hyun Kim, Thomas Koberda, J. de la Nuez González

Let $M$ and $N$ be smooth manifolds, with $M$ closed and connected. If the $C^{r}$ --diffeomorphism group of $M$ is elementarily equivalent to the $C^{s}$ --diffeomorphism group of $N$ f…

math.GR2023

First order rigidity of homeomorphism groups of manifolds

Sang-hyun Kim, Thomas Koberda, J. de la Nuez González

For every compact, connected manifold $M$ , we prove the existence of a sentence $ϕ_{M}$ in the language of groups such that the homeomorphism group of another compact manifold $N$ sa…

math.NT2022

Optimal independent generating system for the congruence subgroups $Γ_{0} (p)$ and $Γ_{0} (p^{2})$

Nhat Minh Doan, Sang-hyun Kim, Mong Lung Lang +1

Let $n$ be a prime or its square. We prove that the congruence subgroup $Γ_{0} (n)$ admits a free product decomposition into cyclic factors in such a way that the $(2, 1)$ -component of…

math.GR2021

Structure and regularity of group actions on one-manifolds

Sang-hyun Kim, Thomas Koberda

In this monograph, we give an account of the relationship between the algebraic structure of finitely generated and countable groups and the regularity with which they act on manif…

math.GR2021

Virtual critical regularity of mapping class group actions on the circle

Sang-hyun Kim, Thomas Koberda, Cristóbal Rivas

We show that if $G_{1}$ and $G_{2}$ are non-solvable groups, then no $C^{1, τ}$ action of $(G_{1} \times G_{2}) * Z$ on $S^{1}$ is faithful for $τ > 0$ . As a corollary, if $S$ is an orien…

math.GR2020

Direct products, overlapping actions, and critical regularity

Sang-hyun Kim, Thomas Koberda, Cristóbal Rivas

We address the problem of computing the critical regularity of groups of homeomorphisms of the interval. Our main result is that if $H$ and $K$ are two non-solvable groups then a f…

math.GT2020

Shapes of hyperbolic triangles and once-punctured torus groups

Sang-hyun Kim, Thomas Koberda, Jaejeong Lee +3

Let $Δ$ be a hyperbolic triangle with a fixed area $φ$ . We prove that for all but countably many $φ$ , generic choices of $Δ$ have the property that the group generated by the $π$ --…

math.GT2019★ 2 cited

Small $C^{1}$ actions of semidirect products on compact manifolds

Christian Bonatti, Sang-hyun Kim, Thomas Koberda +1

Let $T$ be a compact fibered $3$ --manifold, presented as a mapping torus of a compact, orientable surface $S$ with monodromy $ψ$ , and let $M$ be a compact Riemannian manifold. Our…

math.DS2019

Integrability of moduli and regularity of Denjoy counterexamples

Sang-hyun Kim, Thomas Koberda

We study the regularity of exceptional actions of groups by $C^{1, α}$ diffeomorphisms on the circle, i.e. ones which admit exceptional minimal sets, and whose elements have first d…

math.GT2019

Some groups with planar boundaries

Sang-hyun Kim, Genevieve S. Walsh

In this expository note, we illustrate phenomena and conjectures about boundaries of hyperbolic groups by considering the special cases of certain amalgams of hyperbolic groups. Wh…

math.GR2019★ 2 cited

Algebraic Structure of Diffeomorphism Groups of One-Manifolds

Jaewon Chang, Sang-hyun Kim, Thomas Koberda

It is a celebrated result of Mather that the group of $C^{k}$ --diffeomorphisms of an $n$ --manifold is simple, provided that a mild isotopy condition is satisfied, with the possible e…

math.GR2019

Non-freeness of groups generated by two parabolic elements with small rational parameters

Sang-hyun Kim, Thomas Koberda

Let $q \in C$ , let \[a=\begin{pmatrix} 1&0\\1&1\end{pmatrix},\quad b_q=\begin{pmatrix} 1&q\\0&1\end{pmatrix},\] and let $G_{q} < SL_{2} (C)$ be the group generate…

math.GR2017★ 4 cited

Diffeomorphism groups of critical regularity

Sang-hyun Kim, Thomas Koberda

Let $M$ be the circle or a compact interval, and let $α = k + τ \geq 1$ be a real number such that $k = ⌊ α ⌋$ . We write $Diff_{+}^{α} (M)$ for the group of $C^{k}$ diffeomorph…

math.GR2017

Finite subgraphs of an extension graph

Sang-hyun Kim, Thomas Koberda, Juyoung Lee

Let $Γ$ be a finite graph and let $Γ^{e}$ be its extension graph. We inductively define a sequence ${Γ_{i}}$ of finite induced subgraphs of $Γ^{e}$ through succes…

math.GR2017★ 13 cited

Free products and the algebraic structure of diffeomorphism groups

Sang-hyun Kim, Thomas Koberda

Let $M$ be a compact one--manifold, and let $Diff^{1 + bv} (M)$ denote the group of $C^{1}$ orientation preserving diffeomorphisms of $M$ whose first derivatives have…

math.GT2016★ 3 cited

Chain groups of homeomorphisms of the interval

Sang-hyun Kim, Thomas Koberda, Yash Lodha

We introduce and study the notion of a chain group of homeomorphisms of a one-manifold, which is a certain generalization of Thompson's group $F$ . The resulting class of groups exh…

math.GT2016

Flexibility of group actions on the circle

Sang-hyun Kim, Thomas Koberda, Mahan Mj

In this partly expository monograph we develop a general framework for producing uncountable families of exotic actions of certain classically studied groups acting on the circle.…

math.GT2016

Exotic mapping class group actions on the circle

Sang-hyun Kim, Thomas Koberda

It has been known since the time of Nielsen that the mapping class group $Mod_{g, 1}$ of a surface of genus $g$ and one puncture acts faithfully by homeomorphisms on the circ…

math.GT2016

Unsmoothable group actions on compact one-manifolds

Hyungryul Baik, Sang-hyun Kim, Thomas Koberda

We show that no finite index subgroup of a sufficiently complicated mapping class group or braid group can act faithfully by $C^{1 + bv}$ diffeomorphisms on the circle, whic…

math.GT2014★ 7 cited

Right-angled Artin subgroups of the $C^{\infty}$ diffeomorphism group of the real line

Hyungryul Baik, Sang-hyun Kim, Thomas Koberda

We prove that every right-angled Artin group embeds into the $C^{\infty}$ diffeomorphism group of the real line. As a corollary, we show every limit group, and more generally every…

math.GR2013★ 29 cited

Anti-trees and right-angled Artin subgroups of braid groups

Sang-hyun Kim, Thomas Koberda

We prove that an arbitrary right-angled Artin group $G$ admits a quasi-isometric group embedding into a right-angled Artin group defined by the opposite graph of a tree. Consequent…

A note on the proof of nonamenability of F

Hyperbolicity and obstructions to PL actions of the circle

Small growth rates of free groups

Elementary equivalence and diffeomorphism groups of smooth manifolds

First order rigidity of homeomorphism groups of manifolds

Optimal independent generating system for the congruence subgroups Γ0​(p) and Γ0​(p2)

Structure and regularity of group actions on one-manifolds

Virtual critical regularity of mapping class group actions on the circle

Direct products, overlapping actions, and critical regularity

Shapes of hyperbolic triangles and once-punctured torus groups

Small C1 actions of semidirect products on compact manifolds

Integrability of moduli and regularity of Denjoy counterexamples

Some groups with planar boundaries

Algebraic Structure of Diffeomorphism Groups of One-Manifolds

Non-freeness of groups generated by two parabolic elements with small rational parameters

Diffeomorphism groups of critical regularity

Finite subgraphs of an extension graph

Free products and the algebraic structure of diffeomorphism groups

Chain groups of homeomorphisms of the interval

Flexibility of group actions on the circle

Exotic mapping class group actions on the circle

Unsmoothable group actions on compact one-manifolds

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

Anti-trees and right-angled Artin subgroups of braid groups

Optimal independent generating system for the congruence subgroups $Γ_{0} (p)$ and $Γ_{0} (p^{2})$

Small $C^{1}$ actions of semidirect products on compact manifolds

Right-angled Artin subgroups of the $C^{\infty}$ diffeomorphism group of the real line