We study the algorithmic content of Pontryagin -van Kampen duality. We prove that the process of dualization is computable in the important cases of compact and locally compact totally disconnected Polish abelian groups. The applications of our main results include solutions to questions of Kihara and Ng about presentations of connected Polish spaces, and an unexpected arithmetical characterisation of direct products of solenoid groups among all Polish groups.

Martino Lupini, A.M. (2023). Computable topological abelian groups. JOURNAL OF ALGEBRA, 615, 278-327 [10.1016/j.jalgebra.2022.10.003].

Computable topological abelian groups

Martino Lupini;
2023

Abstract

We study the algorithmic content of Pontryagin -van Kampen duality. We prove that the process of dualization is computable in the important cases of compact and locally compact totally disconnected Polish abelian groups. The applications of our main results include solutions to questions of Kihara and Ng about presentations of connected Polish spaces, and an unexpected arithmetical characterisation of direct products of solenoid groups among all Polish groups.
2023
Martino Lupini, A.M. (2023). Computable topological abelian groups. JOURNAL OF ALGEBRA, 615, 278-327 [10.1016/j.jalgebra.2022.10.003].
Martino Lupini, Alexander Melnikov, Andre Nies
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11585/968970
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