103 citations · 240 across the 31 of their papers we have counts for
10 papers · 1 filter
Shapes of hyperbolic triangles and once-punctured torus groups
Sang-hyun Kim, Thomas Koberda, Jaejeong Lee +3
Let be a hyperbolic triangle with a fixed area . We prove that for all but countably many , generic choices of have the property that the group generated by the --…
Small actions of semidirect products on compact manifolds
Christian Bonatti, Sang-hyun Kim, Thomas Koberda +1
Let be a compact fibered --manifold, presented as a mapping torus of a compact, orientable surface with monodromy , and let be a compact Riemannian manifold. Our…
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…
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 . The resulting class of groups exh…
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.…
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 of a surface of genus and one puncture acts faithfully by homeomorphisms on the circ…
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 diffeomorphisms on the circle, whic…
Right-angled Artin subgroups of the diffeomorphism group of the real line
Hyungryul Baik, Sang-hyun Kim, Thomas Koberda
We prove that every right-angled Artin group embeds into the diffeomorphism group of the real line. As a corollary, we show every limit group, and more generally every…
Right-angled Artin groups and finite subgraphs of curve graphs
Sang-hyun Kim, Thomas Koberda
We show that for a sufficiently simple surface , a right-angled Artin group embeds into $\Mod(S)$ if and only if embeds into the curve graph $\mC(S)$ as an induced su…
An obstruction to embedding right-angled Artin groups in mapping class groups
Sang-hyun Kim, Thomas Koberda
For every orientable surface of finite negative Euler characteristic, we find a right-angled Artin group of cohomological dimension two which does not embed into the associated map…