103 citations · 240 across the 31 of their papers we have counts for
22 papers · 1 filter
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.
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…
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…
Elementary equivalence and diffeomorphism groups of smooth manifolds
Sang-hyun Kim, Thomas Koberda, J. de la Nuez González
Let and be smooth manifolds, with closed and connected. If the --diffeomorphism group of is elementarily equivalent to the --diffeomorphism group of f…
First order rigidity of homeomorphism groups of manifolds
Sang-hyun Kim, Thomas Koberda, J. de la Nuez González
For every compact, connected manifold , we prove the existence of a sentence in the language of groups such that the homeomorphism group of another compact manifold sa…
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…
Virtual critical regularity of mapping class group actions on the circle
Sang-hyun Kim, Thomas Koberda, Cristóbal Rivas
We show that if and are non-solvable groups, then no action of on is faithful for . As a corollary, if is an orien…
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 and are two non-solvable groups then a f…
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 --diffeomorphisms of an --manifold is simple, provided that a mild isotopy condition is satisfied, with the possible e…
Non-freeness of groups generated by two parabolic elements with small rational parameters
Sang-hyun Kim, Thomas Koberda
Let , let \[a=\begin{pmatrix} 1&0\\1&1\end{pmatrix},\quad b_q=\begin{pmatrix} 1&q\\0&1\end{pmatrix},\] and let be the group generate…
Diffeomorphism groups of critical regularity
Sang-hyun Kim, Thomas Koberda
Let be the circle or a compact interval, and let be a real number such that . We write for the group of diffeomorph…
Finite subgraphs of an extension graph
Sang-hyun Kim, Thomas Koberda, Juyoung Lee
Let be a finite graph and let be its extension graph. We inductively define a sequence of finite induced subgraphs of through succes…
Free products and the algebraic structure of diffeomorphism groups
Sang-hyun Kim, Thomas Koberda
Let be a compact one--manifold, and let denote the group of orientation preserving diffeomorphisms of whose first derivatives have…
Anti-trees and right-angled Artin subgroups of braid groups
Sang-hyun Kim, Thomas Koberda
We prove that an arbitrary right-angled Artin group admits a quasi-isometric group embedding into a right-angled Artin group defined by the opposite graph of a tree. Consequent…
The geometry of the curve graph of a right-angled Artin group
Sang-hyun Kim, Thomas Koberda
We develop an analogy between right-angled Artin groups and mapping class groups through the geometry of their actions on the extension graph and the curve graph respectively. The…
Surface subgroups of graph products of groups
Sang-hyun Kim
A graph product kernel means the kernel of the natural surjection from a graph product to the corresponding direct product. We prove that a graph product kernel of countable groups…
Embedability between right-angled Artin groups
Sang-hyun Kim, Thomas Koberda
In this article we study the right-angled Artin subgroups of a given right-angled Artin group. Starting with a graph $\gam$, we produce a new graph through a purely combinatorial p…
Hyperbolic surface subgroups of one-ended doubles of free groups
Sang-hyun Kim, Sang-il Oum
Gromov asked whether every one-ended word-hyperbolic group contains a hyperbolic surface group. We prove that every one-ended double of a free group has a hyperbolic surface subgro…
Geometricity and Polygonality in Free Groups
Sang-hyun Kim
Gordon and Wilton recently proved that the double D of a free group F amalgamated along a cyclic subgroup C of F contains a surface group if a generator w of C satisfies a certain…
Polygonal words in free groups
Sang-hyun Kim, Henry Wilton
A longstanding question of Gromov asks whether every one-ended word-hyperbolic group contains a subgroup isomorphic to the fundamental group of a closed hyperbolic surface. An infi…
On right-angled Artin groups without surface subgroups
Sang-hyun Kim
We study the class N of graphs, the right-angled Artin groups defined on which do not contain surface subgroups. We prove that a presumably smaller class N' is closed under amalgam…
Co-contractions of Graphs and Right-angled Artin Groups
Sang-hyun Kim
We define an operation on finite graphs, called co-contraction. By showing that co-contraction of a graph induces an injective map between right-angled Artin groups, we exhibit a f…