Sang-hyun Kim

collaborators

4 papers

math.GR2026

Hyperbolicity and obstructions to PL actions of the circle

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

We investigate acylindrically hyperbolic groups acting on the circle by piecewise linear homeomorphisms. We prove that a finitely generated acylindrically hyperbolic group acting f…

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.GR2026

Elementary equivalence and diffeomorphism groups of smooth manifolds

Sang-hyun Kim, Thomas Koberda, J. de la Nuez GonzÃ¡lez

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.GR2025

First order rigidity of homeomorphism groups of manifolds

Sang-hyun Kim, Thomas Koberda, J. de la Nuez GonzÃ¡lez

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