7 papers
Set theory, logic, and homeomorphism groups of manifolds
James E. Hanson, Thomas Koberda, J. de la Nuez González +1
We investigate the relationship between axiomatic set theory and the first-order theory of homeomorphism groups of manifolds in the language of group theory, concentrating on first…
Group topologies on groups of bi-absolutely continuous homeomorphisms
J. de la Nuez González
The group of homeomorphisms of the closed interval that are absolutely continuous and have an absolutely continuous inverse was shown by Solecki to admit a natural Polish group top…
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.…
The compact-open topology on the diffeomorphism or homeomorphism group of a smooth manifold without boundary is minimal in almost all dimensions
J. de la Nuez González
We show that for any connected smooth manifold of dimension different from the restriction of the compact-open topology to the diffeomorphism group of is minimal, i.e.…
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…
The model theory of the curve graph
Valentina Disarlo, Thomas Koberda, J. de la Nuez González
In this paper we develop a bridge between model theory, geometric topology, and geometric group theory. In particular, we investigate the Ivanov Metaconjecture from the point of vi…
Group topologies on automorphism groups of homogeneous structures
Zaniar Ghadernezhad, Javier de la Nuez González
We classify all group topologies coarser than the topology of stabilizers of finite sets in the case of automorphism groups of countable free-homogeneous structures, Urysohn space…