3 papers
math.GT2025
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…
math.GN2024
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…
math.GR2023
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.…