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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.GT2023
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.…
math.GT2020
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…