8 papers · 1 filter
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…
Linearity criteria for automorphism groups of malabelian groups
Thomas Koberda, Mark Pengitore
Let be a finitely generated malabelian group, let be a finitely generated subgroup, and let denote the preimage of in . W…
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…
Generic torsion-free groups and Rubin actions
Thomas Koberda, Yash Lodha
We use model theoretic forcing to prove that a generic countable torsion-free group does not admit any nontrivial locally moving action on a Hausdorff topological space, and yet ad…
Uniform first order interpretation of the second order theory of countable groups of homeomorphisms
Thomas Koberda, J. de la Nuez González
We show that the first order theory of the homeomorphism group of a compact manifold interprets the full second order theory of countable groups of homeomorphisms of the manifold.…
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 s…